Assignment_2_ComputationalModellingBehaviouralData.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "statewide-stuff",
   "metadata": {},
   "source": [
    "# Assignment 2 code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "educational-function",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib\n",
    "import sys\n",
    "import math\n",
    "import random\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.animation as animation\n",
    "import pandas as pd\n",
    "import time\n",
    "import scipy as sp\n",
    "from scipy import ndimage\n",
    "from tqdm import tqdm\n",
    "from scipy import optimize\n",
    "from scipy import stats\n",
    "from scipy.stats import multivariate_normal\n",
    "\n",
    "font = {'fontname': 'serif'}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "maritime-cincinnati",
   "metadata": {},
   "source": [
    "## Task (a): Exploring the data \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "intimate-banner",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mean STAI-Y2 score is: 45.42\n",
      "The standard deviation of the STAI-Y2 scores is: 15.92368\n",
      "The median of the STAI-Y2 scores is: 42.5\n",
      "The patients classified as healthy controls are the following ones: [22. 26. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43.\n",
      " 44. 45. 46. 47. 48. 49. 50.]\n"
     ]
    }
   ],
   "source": [
    "#Parameters\n",
    "cutoff = 43\n",
    "\n",
    "#Open STAI-Y2 score file\n",
    "StaiScores = pd.read_csv(\"stai_scores.csv\", header = None, index_col = None)\n",
    "\n",
    "#Print mean, std and median\n",
    "print(\"The mean STAI-Y2 score is: \" + str(np.mean(StaiScores).to_string(index = False)))\n",
    "print(\"The standard deviation of the STAI-Y2 scores is: \" + str(np.std(StaiScores).to_string(index = False)))\n",
    "print(\"The median of the STAI-Y2 scores is: \" + str(np.median(StaiScores)))\n",
    "\n",
    "\n",
    "#Classify patients\n",
    "healthy_index = []\n",
    "for i in range(len(StaiScores)):\n",
    "    if float(StaiScores.loc[i].to_string(index = False)) <= 43:\n",
    "        healthy_index.append(i)\n",
    "        \n",
    "print(\"The patients classified as healthy controls are the following ones: \" + str(healthy_index + np.ones(len(healthy_index))))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "comparative-magic",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of times each participant choose option A: [29. 40. 55. 15. 46. 36. 55. 39. 30. 33. 44. 27. 27. 32. 43. 39. 15. 23.\n",
      " 48. 48. 28. 41. 39. 24. 61. 33. 48. 47. 38. 22. 66. 40. 34. 46. 35. 51.\n",
      " 37. 33. 65. 50. 29. 26. 34. 55. 23. 58. 27. 28. 41. 22.]\n",
      "Average percentage of number of times option A is chosen: 23.8125\n"
     ]
    }
   ],
   "source": [
    "choices = pd.read_csv(\"inst_choices.csv\", header = None, index_col = None)\n",
    "outcomes = pd.read_csv(\"inst_outcomes.csv\", header = None, index_col = None)\n",
    "#Number of times each participant choose option A\n",
    "NumAopt = np.empty(len(StaiScores)) \n",
    "\n",
    "for i in range(len(StaiScores)):\n",
    "    NumAopt[i] = len(np.where(choices.loc[i] == 1)[0])\n",
    "\n",
    "print(\"Number of times each participant choose option A: \" + str(NumAopt))\n",
    "\n",
    "print(\"Average percentage of number of times option A is chosen: \" + str((np.sum(NumAopt)/50)*(100/160)))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "architectural-drove",
   "metadata": {},
   "source": [
    "## Task (b): Simulations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "theoretical-architect",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 10000/10000 [00:11<00:00, 877.41it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The average number of aversive sounds is: 60.8977\n"
     ]
    }
   ],
   "source": [
    "#Simulation Parameters\n",
    "trials = 160\n",
    "N = 10000\n",
    "\n",
    "#Simulation function of Model 1\n",
    "def model_simulate(alpha, beta, V_0):  \n",
    "    \n",
    "    c = np.zeros(trials)\n",
    "    o = np.zeros(trials)\n",
    "    V_a = np.zeros(trials)\n",
    "    V_b = np.zeros(trials)\n",
    "    \n",
    "    #Initial conditions\n",
    "    V_a[0] = V_0\n",
    "    V_b[0] = V_0\n",
    "    \n",
    "    #First 40 trial set\n",
    "    for t in range(0,40):\n",
    "        \n",
    "        #Probability of choosing A\n",
    "        p_choose_A = 1/(1 + np.exp(beta*(V_a[t]-V_b[t])))\n",
    "        \n",
    "        #If A is chosen\n",
    "        if np.random.rand() < p_choose_A:\n",
    "            \n",
    "            c[t] = 1 \n",
    "            \n",
    "            #Will give aversive outcome with p = 0.6\n",
    "            if np.random.rand() < 0.6:\n",
    "                \n",
    "                o[t] = 1\n",
    "            \n",
    "            #Update V_a but not V_b\n",
    "            V_a[t+1] =  np.copy(V_a[t] + alpha*(o[t] - V_a[t]))\n",
    "            V_b[t+1] =  np.copy(V_b[t]) \n",
    "        \n",
    "        #If B is chosen\n",
    "        else:\n",
    "            \n",
    "            c[t] = 2\n",
    "            \n",
    "            #Will give aversive outcome with p = 0.4\n",
    "            if np.random.rand() < 0.4:\n",
    "                \n",
    "                o[t] = 1\n",
    "        \n",
    "            #Update V_b but not V_a\n",
    "            V_a[t+1] =  np.copy(V_a[t]) \n",
    "            V_b[t+1] =  np.copy(V_b[t] + alpha*(o[t] - V_b[t]))\n",
    "                \n",
    "    #Second 40 trial set\n",
    "    for t in range(40,80):\n",
    "        \n",
    "        #Probability of choosing A\n",
    "        p_choose_A = 1/(1 + np.exp(beta*(V_a[t]-V_b[t])))\n",
    "        \n",
    "        if np.random.rand() < p_choose_A:\n",
    "            \n",
    "            c[t] = 1\n",
    "            \n",
    "            if np.random.rand() < 0.8:\n",
    "            \n",
    "                o[t] = 1\n",
    "            \n",
    "            V_a[t+1] =  np.copy(V_a[t] + alpha*(o[t] - V_a[t]))\n",
    "            V_b[t+1] =  np.copy(V_b[t]) \n",
    "            \n",
    "        else:\n",
    "            \n",
    "            c[t] = 2\n",
    "            \n",
    "            if np.random.rand() < 0.2:\n",
    "                \n",
    "                o[t] = 1\n",
    "        \n",
    "            V_a[t+1] =  np.copy(V_a[t]) \n",
    "            V_b[t+1] =  np.copy(V_b[t] + alpha*(o[t] - V_b[t]))\n",
    "                \n",
    "    #Third 40 trial set        \n",
    "    for t in range(80,120):\n",
    "        \n",
    "        p_choose_A = 1/(1 + np.exp(beta*(V_a[t]-V_b[t])))\n",
    "        \n",
    "        if np.random.rand() < p_choose_A:\n",
    "            \n",
    "            c[t] = 1\n",
    "            \n",
    "            if np.random.rand() < 0.6:\n",
    "                \n",
    "                o[t] = 1\n",
    "            \n",
    "            V_a[t+1] =  np.copy(V_a[t] + alpha*(o[t] - V_a[t]))\n",
    "            V_b[t+1] =  np.copy(V_b[t])\n",
    "            \n",
    "        else:\n",
    "            \n",
    "            c[t] = 2\n",
    "            \n",
    "            if np.random.rand() < 0.4:\n",
    "            \n",
    "                o[t] = 1\n",
    "        \n",
    "            V_a[t+1] =  np.copy(V_a[t]) \n",
    "            V_b[t+1] =  np.copy(V_b[t] + alpha*(o[t] - V_b[t]))     \n",
    "    \n",
    "    #Fourth 40 trial set         \n",
    "    for t in range(120,159):\n",
    "        \n",
    "        p_choose_A = 1/(1 + np.exp(beta*(V_a[t]-V_b[t])))\n",
    "        \n",
    "        if np.random.rand() < p_choose_A:\n",
    "            \n",
    "            c[t] = 1\n",
    "            \n",
    "            if np.random.rand() < 0.65:\n",
    "                \n",
    "                o[t] = 1\n",
    "            \n",
    "            V_a[t+1] =  np.copy(V_a[t] + alpha*(o[t] - V_a[t]))\n",
    "            V_b[t+1] =  np.copy(V_b[t])\n",
    "            \n",
    "        else:\n",
    "            \n",
    "            c[t] = 2\n",
    "            \n",
    "            if np.random.rand() < 0.35:\n",
    "                \n",
    "                o[t] = 1\n",
    "\n",
    "            V_a[t+1] =  np.copy(V_a[t]) \n",
    "            V_b[t+1] =  np.copy(V_b[t] + alpha*(o[t] - V_b[t]))     \n",
    "    \n",
    "    #Last trial\n",
    "    p_choose_A = 1/(1 + np.exp(beta*(V_a[159]-V_b[159])))\n",
    "    \n",
    "    if np.random.rand() < p_choose_A:\n",
    "            \n",
    "        c[159] = 1\n",
    "            \n",
    "        if np.random.rand() < 0.65:\n",
    "                \n",
    "            o[159] = 1\n",
    "    else:\n",
    "            \n",
    "        c[159] = 2\n",
    "            \n",
    "        if np.random.rand() < 0.35:\n",
    "                \n",
    "            o[159] = 1\n",
    "    \n",
    "    return c, o, V_a, V_b\n",
    "\n",
    "choices_vals = np.zeros((N,trials))\n",
    "o_vals = np.zeros((N,trials))\n",
    "V_a_vals = np.zeros((N,trials))\n",
    "V_b_vals = np.zeros((N,trials))\n",
    "V_a_minus_V_b_vals = np.zeros((N,trials))\n",
    "\n",
    "\n",
    "for n in tqdm(range(N)):\n",
    "    \n",
    "    choices_vals[n,:] , o_vals[n,:] , V_a_vals[n,:] , V_b_vals[n,:] = model_simulate(0.3,8,0.5)\n",
    "    \n",
    "    V_a_minus_V_b_vals[n,:] = V_a_vals[n,:] - V_b_vals[n,:]\n",
    "    \n",
    "choices_average = np.average(choices_vals,axis=0)\n",
    "o_average = np.average(np.sum(o_vals,axis=1)) #np.average(o_vals,axis=0)\n",
    "V_a_average = np.average(V_a_vals,axis=0)\n",
    "V_b_average = np.average(V_b_vals,axis=0) \n",
    "V_a_minus_V_b_average = np.average(V_a_minus_V_b_vals,axis=0)    \n",
    "\n",
    "print(\"The average number of aversive sounds is: \" + str(o_average))#str(np.sum(o_average)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "perceived-guess",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 777.6x446.4 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 777.6x446.4 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 921.6x518.4 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Plotting\n",
    "\n",
    "f1,ax = plt.subplots(figsize=(10.8, 6.2));\n",
    "ax.plot(np.arange(trials),V_a_average,label = 'Value of stimulus A')\n",
    "ax.plot(np.arange(trials),V_b_average,label = 'Value of stimulus B')\n",
    "ax.axvline(x=40,linestyle = ':')\n",
    "ax.axvline(x=80,linestyle = ':')\n",
    "ax.axvline(x=120,linestyle = ':')\n",
    "ax.axvline(x=160,linestyle = ':')\n",
    "ax.tick_params(axis='both', which='major', labelsize=15)\n",
    "ax.legend(fontsize=15,loc = 'lower right')\n",
    "plt.title(\"Average evolution of V(A) and V(B) across 160 trials\",fontsize=20,**font)\n",
    "plt.xlabel(\"Trials\",fontsize=20,**font)\n",
    "plt.ylabel(\"Value of stimulus\",fontsize=20,**font)\n",
    "plt.show()\n",
    "\n",
    "f2,ax = plt.subplots(figsize=(10.8, 6.2));\n",
    "ax.plot(np.arange(trials),V_a_minus_V_b_average)\n",
    "ax.axvline(x=40,linestyle = ':')\n",
    "ax.axvline(x=80,linestyle = ':')\n",
    "ax.axvline(x=120,linestyle = ':')\n",
    "ax.axvline(x=160,linestyle = ':')\n",
    "ax.tick_params(axis='both', which='major', labelsize=15)\n",
    "plt.title(\"Average evolution of V(A) - V(B) across 160 trials\",fontsize=20,**font)\n",
    "plt.xlabel(\"Trials\",fontsize=20,**font)\n",
    "plt.ylabel(\"V(A) - V(B)\",fontsize=20,**font)\n",
    "plt.show()\n",
    "\n",
    "\n",
    "f3,ax = plt.subplots(figsize=(12.8, 7.2));\n",
    "ax.plot(np.arange(trials),choices_average)\n",
    "ax.axvline(x=40,linestyle = ':')\n",
    "ax.axvline(x=80,linestyle = ':')\n",
    "ax.axvline(x=120,linestyle = ':')\n",
    "ax.axvline(x=160,linestyle = ':')\n",
    "plt.title(\"Average choice\",fontsize=20,**font)\n",
    "plt.xlabel(\"Trials\",fontsize=20,**font)\n",
    "plt.ylabel(\"Choice\",fontsize=20,**font)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "municipal-tactics",
   "metadata": {},
   "source": [
    "## Task (c): Exploring parameter settings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "unnecessary-filter",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 30/30 [16:27<00:00, 32.92s/it]\n"
     ]
    }
   ],
   "source": [
    "N = 1000\n",
    "\n",
    "alphas_hm = np.linspace(0.01,1,30,endpoint=False)\n",
    "betas_hm = np.linspace(0.01,15,30)\n",
    "\n",
    "choices_vals_hm = np.zeros((N,trials))\n",
    "o_vals_hm = np.zeros((N,trials))\n",
    "V_a_vals_hm = np.zeros((N,trials))\n",
    "V_b_vals_hm = np.zeros((N,trials))\n",
    "\n",
    "o_heatmap = np.zeros((len(alphas_hm),len(betas_hm)))\n",
    "\n",
    "for a in tqdm(range(len(alphas_hm))):\n",
    "    for b in range(len(betas_hm)):\n",
    "        for n in range(N):\n",
    "    \n",
    "            choices_vals_hm[n,:] , o_vals_hm[n,:] , V_a_vals_hm[n,:] , V_b_vals_hm[n,:] = model_simulate(alphas_hm[a],betas_hm[b],0.5)\n",
    "       \n",
    "        o_heatmap[b,a] = np.average(np.sum(o_vals_hm,axis = 1)) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "absolute-pickup",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x7f54c1a73f70>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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SW3Wouj3K70mHTbWWloAOlDr1nUwKa0eF0zols08Cn2xYvI08jHeD7VqykM/1+VVkMk4Xs8LhB0EQdBeDWvq7gH4jHH4QBEGbZPHlO9PC7ybh8IMgCNrFajDZEZVOVwmHHwRBMB2ihR8EQTD7EYZ8ssu+Ihx+EARBu5hBOHw/ks4D3gw8aWaHNaz7Y+BvgT3NbH0qrZKM0XJrOZYnaqQn+mSttjlpI0e0wkppftKmWtvScr0nnHOt5ogqWWotBQQYrixK2kw68ppM1Algt4H90+k4pK/zSnskbSY6JKccY2HSxnO8UiGJN1tacrlHKR3Z1MOQI66xI1gmnsjakw7J5YSlbQbLaflwZ5iZDr+XX9qeD+wUJ1rSAWThPh/tdoGCIAhcmKHqtuTUb/TM4ZvZ9cDPmqz6LPBxfCOEBEEQ9ICsDz819Rt91Ycv6VjgcTO7IzXCUh5mdCXAbuX0V5dBEASdw6DWre6jztE3Dl/SKHAG8EaPvZmdQxZzgv2G9oqngSAIuke8tN1lXkgWE7reut8fuE3SEWb2056WLAiCoAFFC3/6mNmPKIzqImk1sMyj0gmCIOgqFl06bSHpIuC1ZEOArQE+aWZfmn56rdcPlRck0xif3JC0MdKPcQMOOaBnwO+BgcUt13skjjjyKTkiWI5XHZEnHVQckkGP5NIT4dODZ4Dy1MDiAGVL72ePLNMzuH2KCUvnM7/SvUt/yHGoKqV0vT1HXF3TehiaTEtk+42eOXwzOyGx/sAuFSUIgqAtZBZdOkEQBHOGcPhBEARzgA618CUdAlxSWPQC4M+AVwKH5MsWAhvMbGmT7VcDG4EqMNlqwHQIhx8EQTA9OuDwzex+YCmAsvgvjwOXm9lZdRtJnwF+0SKZ13nFLeHwgyAI2sZQrePDKS4HHjKzR+oL8oHN3wG8vhMZhMMPgiBoFzPwqXQWS7qlMH9O/tFoM44HLmpY9irgCTN7YKqSAFdLMuCfWqQNzBKHXxIMJwYvrlp6/Ek5BgUfrOyZtBmfTA/CXfYMwl1t9RTni3JZc0gczSHjq5TTcsqqI1rmoCMMxmbH/ls08Px0eRwS2mHS+9AjuawqnZcnnXJCfDjPIbMdLKUjw5YdISxHHN7BM0C5J1rmcDmd0Fgl3YXikXd2CjmuG2B9ql8dQNIgcCzwiYZVJ7DzTaDIkWa2VtJewDWS7svjlDVlVjj8IAiCrtL5D6+OAW4zsyfqCyRVgLcBh09dDFub/39S0uXAEcCUDr+X4ZGDIAhmLrVaevLTrCX/BuA+M1vTbANJY5Lm13+TxSG7q1Um4fCDIAjaxaxjDj8PHHkU8PWGVTv16UvaV9KqfHYJcIOkO4AfAP9qZle1yiu6dIIgCNrG0GT6vaArJbPNwE7xWMzspCbL1gIr8t8PAy9tJ69w+EEQBO1itNtl0xeEww+CIGgbC4cfBEEwJzAilk6vEFBO6G/LDo29WfoAZnLZ1pQ0nLTBESo3FUJZSr9zHyrvnrTxpCPS2u5KJa3V94Q19oSyniSt+R8irfnfhifEdNpk1OanjRxsUeuPeeY5zr+qRxzvYMLRgN3TcaqPOjT2VXPs5D5Cz82Xts85s8LhB0EQdJ1w+EEQBHMAM5iMMW2DIAhmPwbUuhfGoVOEww+CIJgO0aUTBEEwF5iZssyehVaQdJ6kJyXdVVj2t5Luk3SnpMslLexV+YIgCKak3qWTmvqMXrbwzwc+D1xQWHYN8Akzm5T0N2ShQk9LJVSSMb/S+gXKgNKSwaHKwqTNRHVT0mZ4YHHSZtvkz5I2IwNLkjYpao6w0J7wyAPl0aSNR3JZckhAPdQcElqPnLLkKHOZtKR3yBxySdJlHrLWeU045LyjjvDI2xzOaLic3oEbHdEFPKGYFw6m942nPT1R62Ib1hceua/oWQs/j9n8s4ZlV5tZ3XPfCOzf9YIFQRCkMIPJWnrqM/q5D/997Di47w5IWgmsBNijkv7AJgiCoKP0YZdNir4MjyzpDGASuHAqGzM7x8yWmdmyeRXPl61BEASdwSzr0UlN/UbftfAlnQi8GVhu1qFvxIMgCDpNtPB3DUlHk72kPTaPER0EQdB/GNlb5NSUQNIhkm4vTM9IOlXSpyQ9Xli+Yortj5Z0v6QHJZ2eyq9nLXxJFwGvJRvVfQ3wSTJVzhDZYLwAN5rZ7/eqjEEQBFPSgWCZZnY/sBRAUhl4HLgcOBn4rJl9eqptc/u/Jxstaw1ws6QrzeyeqbbpmcM3sxOaLP7SdNISUFbrx6thpV/sbszGA25JpZyWd45XNyZtyqV0OlVrHRGyWnNEjHRITT3SzXIicmeWjkPeqbS8c1P16aTNonJa+uqRXHq6WcvWmcuk7Ig4OpKI6jpWTpfFEy1z2CGVnO+o9ojDxtMx6+lq8NiILnWzGFit4xE+lwMPmdkjchwfsgHLH8xHvkLSxcBbgCkdfl916QRBEMwYfF06iyXdUphWtkixcQzbU/KPUM+TtKiJ/X7AY4X5NfmyKQmHHwRBMB1qSk+wvq4mzKdzmiWlbKCNY4FL80VfAF5I1t2zDvhMs82aLGv5iNN3Kp0gCIK+p/NdOscAt5nZEwD1/wCSvgh8s8k2a4ADCvP7Ay37paOFHwRB0DaO1n17N4QTKHTnSNqnsO6twF07bQE3AwdLOih/QjgeuLJVJtHCD4IgaBcDq3amvSxplExp84HC4v8laWmWE6vr6yTtC5xrZivymGOnAN8CysB5ZnZ3q7zC4QdBEEyHDgVqy7852qNh2XumsF0LrCjMrwJWefOaFQ5fGOVSa4GdaxDuUloyaA7x7WA5PaB1yTGoeopyeShpU1HaBoeNR3I5VEpLX80hhJxf3itpUyUtJR1wDGI+5JBceuSd2xKDjwOM1dJS3InE+bXFof0uOyKSeiJhTjoUjp6BzkcrnkHM0+kMltOVHxtwhO/sBNZ2l01fMCscfhAEQbcxC4cfBEEwN+hm7P0OEQ4/CIKgTey5+dL2OSccfhAEQduoYyqdbhIOPwiCoF2M6NIJgiCYK0SXThAEwZxAodLpFSUZY5XW+luPlnqkvDBps9kRutcTtrhK2mY4Edo4C4e963i08R49/9baMx1JZ5KtSZth7Za08RzzsuMS8KQzZIOOvNLpzCu1/j6j7Aib67EZcPRGeMbgHh1yhGIupW1GyunMPB0ok93qZokunSAIgrmBAbV4aRsEQTAHMEULPwiCYK4QL22DIAjmCDPxpW3PnknyYbuelHRXYdnukq6R9ED+v9mwXkEQBL2l3qWTmvqMXpbofODohmWnA9ea2cHAtfl8EARB32E1Jad+o2ddOmZ2vaQDGxa/BXht/vsrwHXAaam0yiVjwVBrKd+i2uJkmUql9P1vspSWU3aKqk22NkitByqltAzSE9a4zK6HcwYYVDoE9SDpMMKe8tQcclMPI7XhpE2p6fCiOzLgkNFuS4ShHiulL9mxSvo8HneEWR50qH7Hq+l6jznCI5ccvnHC0WLeVu2MVDmFWah0OsESM1sHYGbrJE0ZGD0f/X0lwF6DaScSBEHQOYTZrjt8SYcAlxQWvQD4M2A/4LeBceAh4GQz29Bk+9XARqAKTJrZslb5zbxbVI6ZnVMfCX7hgGOQjyAIgk7SgTFtzex+M1tqZkuBw4HNwOXANcBhZvYS4MfAJ1ok87o8jZbOHvrP4T9RH7w3//9kj8sTBEHQFDMlpzZZDjxkZo+Y2dVmv+yzvRHYvxNl7jeHfyVwYv77ROCKHpYlCIKgOeZ+abtY0i2FaWWLVI8HLmqy/H3Av01dEq6WdGsibaCHffiSLiJ7QbtY0hrgk8CZwNckvR94FHh7r8oXBEEwFebvw1/v6WqRNAgcS0PXjaQzgEngwik2PdLM1ubvO6+RdJ+ZXT9VPr1U6ZwwxarlXS1IEARBu3RepXMMcJuZPVFfIOlE4M3AcjNrKnUys7X5/yclXQ4cAfSfw+8shuQY9j7BJjYkbSZqW5I2gw6ZoydCZdVaRwAdLae/S0ulAZ2TXI5oQdLGI5X02CyopfdxTel0xmppCWiN9Lk16LiUas2v2R3YfaB11E1zlMWRDWOOQz7iUDgOltOZlTtwbQIMldNa0oojMmen6PCXtidQ6M6RdDSZJP01Zra52QaSxoCSmW3Mf78R+ItWmfRbH34QBMGMoFMfXkkaBY4Cvl5Y/HlgPlk3ze2S/jG33VfSqtxmCXCDpDuAHwD/amZXtcprlrTwgyAIukcbffjptLIW/B4Ny140he1aYEX++2Hgpe3kFQ4/CIKgXSyiZQZBEMwZan0YHC1FOPwgCIJ2sf4MjpYiHH4QBEGbGDMzHv6scPjCGCy3jhw5z9IRD/epHZi0eariGYQ7HVGzZg6JWWLAb4/kcqLWVNG1Yz7ldJ0GSQeo89R7gaWjlm7VpqSNZ9DwDaUNSRuPTm1BbSydjGPg8BFHtMyttdZS0mFHRFdHsEyqjkCiAw7pZtnh8zwyUQ+DpfQ1U3ZIcTtFp17adpNZ4fCDIAi6TS1a+EEQBHOA6MMPgiCYGxih0gmCIJgzxEvbIAiCuYCJWry0DYIgmP0Y8aVtEATBnCG6dHqEBAOV1jr8kVK6qr9wCIY9oYRHSYcJfkZPJW2gtW7bo8P3MEBah19xnCoemwmNJ21GbX7SxkPZ0uXZ03ZLJ+S4rodLaY39FCHNd2Co1DqzxGoABhw9DUMOG49+ftgRHnm4nNbGV0qesNnpynciTLoLg2q8tA2CIJj9ZNEyo4UfBEEwJ5iJDn/mPZMEQRD0ATVTckoh6ZB8gJP69IykUyXtLukaSQ/k/5sObyfpaEn3S3pQ0ump/PrS4Uv6sKS7Jd0l6SJJ6UA4QRAEXcRMySmdht1vZkvNbClwOLAZuBw4HbjWzA4Grs3nd0BSGfh7svFwDwVOkHRoq/z6zuFL2g/4I2CZmR1G9uby+N6WKgiCYDtmnXH4DSwHHjKzR4C3AF/Jl38F+J0m9kcAD5rZw2Y2Dlycbzcl/dqHXwFGJE0Ao8DaHpcnCIKggLwqncWSbinMn2Nm50xhezzbBzJfYmbrAMxsnaS9mtjvBzxWmF8D/KdWhek7h29mj0v6NPAosAW42syubrSTtBJYCbDP8DBjw1t3Oe9yQgYJPunhNrY48krLO5V4ABvTwnQa5XSdJhxhjT02w8xL2nikkoPmiMvrYH4tXZ5ttJbzAixyhI+WIzwyDhslpIeDDl2mR7o5nD4tmDeQljiOV9OZjTny8lB2SC672WXhbMGvN7NlKSNJg8CxwCfaKEKzArTcSf3YpbOI7LHkIGBfYEzS7zbamdk5ZrbMzJYtGuyMgwiCIPBgdOalbYFjgNvM7Il8/glJ+wDk/59sss0a4IDC/P4kekP6zuEDbwB+YmZPmdkE8HXgN3tcpiAIgu10vg//BLZ35wBcCZyY/z4RuKLJNjcDB0s6KH9COD7fbkr60eE/CrxC0qiy5+TlwL09LlMQBEGBdOve28KXNAocRda4rXMmcJSkB/J1Z+a2+0paBWBmk8ApwLfIfOTXzOzuVnm5+vAlyTzfhXcAM7tJ0mXAbcAk8ENgqpccQRAEXcfIvrbtSFpmm4E9GpY9TdbYbbRdC6wozK8CVnnzSrbwJb0d+JmkSUm3SnqnpJKksyTdJOnTkg70ZujBzD5pZi82s8PM7D1mln5jGARB0EWqtVJy6jc8Jfor4PPAK4D/C3wZ+CZZv9J3gMOAWyQd9hyVMQiCoM9I99/3Y+gFT5fOfsCXzGw1mWNfDZwPnGJmXwCQ9FfA/6D5xwHPOaVSjeGR1rLMvYYckRy3jqbzcsTA3qK0RLTkuNf+QuuTNikGbDBdFqXL4kmn4pBclhyPwR55bNmx/xaU0nLKLbW0LHPC0Zs5VkqXZ7icrns1kZUnEuaAw89srqZthhxyyqGSQyrpKE/FIbmsOhxoOuZmZzCbmYOYe1r4DwFHFuYvzf/fXFh2PtkTQBAEwZxgtrbwzwTOzbtsVpG9RF0G3F+wmQ+MdL54QRAE/YknPn+/kXT4ZvZVSc8AHwX+mOzrroeA2yTdRiYHOgP43nNZ0CAIgn7B/KEV+gqXLNPMvgl8U9II8BJgKfAy4L8Av07Wuv+ppCuAO4E7zezSKZILgiCY8fRjl02KtmLpmNkW4KZ8AkBSCTiE7AawlKwvfyXb+/qDIAhmFUb3XhB3kl0OnmZmNbJunXuBr+5yiYIgCPodmwMt/H6mXGqtM/NEB/Qw4JAeblL63j9i6TFd9qs9r+X6qqONMam0/m6bIxKmJ4LlkEO66ZFTeuq10CG59ESwnFdO12vYIbl0KC5dksrUmOCeNDwtT1e0zEpn2rA1xzf6I+X0eepxsN3sVZ+JssxZ4/CDIAi6SadCK3STcPhBEARtYohJx0eY/UY4/CAIgmkQLfwgCII5QH0AlJlGOPwgCIJ2sSyezkwjHH4QBME0mJWhFYIgCIIdMTqnw5e0EDiXLNS8Ae8DTiX7oBVgIbDBzJY22XY1sBGoApOpAdNnhcMvlWuMzNvc0maeo6a7VdJGQ1VHKOHaoqTNZqW17wOJMMHWeoB6AOY59P6Djm8LUmUBKDvCLFctre0uO05Lj0K8U0Pb+8L7dubiT4UkHvSER3bYLBhInzvbHLFiRsvpIzHgCKHsCX28aHhL0mZkYDxp0xnkKrOTs4GrzOy4fGzaUTN75y9zkj4D/KLF9q8zM1cs9Vnh8IMgCLpJp17aSloAvBo4CcDMxoHxwnoB7wBev8uZ0Z+DmAdBEPQ9NccELJZ0S2Fa2ZDMC4CngC9L+qGkcyWNFda/CnjCzB6YohgGXJ0PP9uY9k70pcOXtFDSZZLuk3SvpFf2ukxBEARFnAOgrDezZYXpnIZkKsDLgS+Y2cuATcDphfUnABe1KMaRZvZy4BjgDyW9ulWZ+9Lhs71P68XAS8kCswVBEPQF9SEOU5ODNcAaM6tHIL6M7AaApArwNuCSqctha/P/TwKXA0e0yqzvHH6hT+tLkPVpmdmGnhYqCIKggaopOaUws58Cj0mqK3KWA/fkv98A3Gdma5ptK2lM0vz6b+CNwF2t8us7h0+6TwsASSvr/WJPb00PRB0EQdAp6vHwHX34Hj4IXCjpTrIxRf46X348Dd05kvaVtCqfXQLcIOkO4AfAv5rZVa0y6keVTr1P64NmdpOks8n6tP60aJT3hZ0DsHTPEasMTrRMdKSSlobtMZS+/z2dVlMyaWkJ47zSvKTNRK31KVNx3K+HS5640GkBY9XxWaEnjPB4ok7gC2tcdth4WjNjlbSVR5Y50qHw2yn5sKO4ri9Ah0rp4zDokFMOO2SZg468hsvpRttkrUM7uSN0bpByM7udbJzwxuUnNVm2FliR/36YrMvbTT+28Kfs0wqCIOgXOtjC7xp95/ATfVpBEAQ9p/6lrUOl01f0Y5cObO/TGgQeBk7ucXmCIAh2wDOSV7/Rlw5/qj6tIAiCfsDMFw6i3+hLhx8EQdDv9GMffYpw+EEQBNOgH/voU8wKhy8ZleHWUfIWDlST6fx8W3p3eGR8HnnihEM7V0ukU3acb5OOfCYcnZGjlbQkbsAhlRx0aBw9kSc9rathh4rPE1nSc1mnolyCL0Jl6lDsPpg+jzdNpitV6ZDkUupMJEwPg6V03Se6JN2s6/BnGrPC4QdBEHSbGPEqCIJgjhAjXgVBEMwBDKjOwD6dcPhBEARto2jhB0EQzAks+vCDIAjmBKHS6SGqVBlc9ExLmz2G0oMbe+RsIw6bja0DdwJgjsfBbQkVmkcKuMExpvOYY2RsjwR01FGezVVPJMx0Oh7JZdXRAvN8Hr9wMG3jGajbQyqV8Vp654xV0q6o1CE55cKB9Mk+UklHwhyrpNMpO6JultU9NxyhFYIgCOYAxswMrdB30TKDIAhmAmbpyUOzMbwlfUrS45Juz6cVU2x7tKT7JT0o6fRmNkWihR8EQTANOth5VB/D+7g8QvAo8Cbgs2b26ak2klQG/h44imwckZslXWlmU4aTjxZ+EARBm2Tx8He9hb+LY3gfATxoZg+b2ThwMfCWVhuEww+CIJgGzhGvFtfH3s6nlQ3JtBrD+xRJd0o6T9KiJkXYD3isML8mXzYl4fCDIAjaxTKVTmoC1pvZssJ0TkNK9TG8v2BmLwM2kY3h/QXghWSDmq8DPtOkFM3eGrd8rgiHHwRB0CaZSic9OWg6hreZPWFmVTOrAV8k675ptu0Bhfn9gbWtMpsVL21VrlFZsLmlzcKhbcl0Nk6md4eUthl2CMm3TKZt9hhqfcZsdWjaxyppm/F01FkGOxR1dsFgZ8TLww7d+4RDNtepFo8nlLBHH59yEpOOOo1U0gfUIykcc+jna450yg7N/7gjrPGIQ4c/5NDzd4pOfGlrZj+V9JikQ8zsfvIxvCXtY2brcrO3Anc12fxm4GBJBwGPA8cD72qV36xw+EEQBN2kw1/aNhvD+3OSluZZrQY+ACBpX+BcM1thZpOSTgG+BZSB88zs7lYZ9a3DzyVHtwCPm9mbe12eIAiCIp360naKMbzfM4XtWmBFYX4VsMqbVz/34X8IuLfXhQiCIGiGOaZ+oy8dvqT9gf8MnNvrsgRBEDRilsXDT039Rl86fOAs4OO06CaTtLKubV3/bD/eS4MgmM04dfh9Rd85fElvBp40s1tb2ZnZOXVt6+J5My+IURAEMxfDrcPvK/rxpe2RwLF5sKBhYIGkfzaz351yCxkaaS0h231kUzLjp7cOJ21GR9KSt00OeefWSvpeq4SczXO39oTT9VBxyCCtQ9EDPTI+T+tpwFH3QUe9OiVzHHDUyxO2OMVIOV1eX6jhdFmGHHmNOKSSo4Np2XS15ghfPuiIB94h+tCfJ+m7Fr6ZfcLM9jezA8l0pf/R0tkHQRD0gGjhB0EQzBFiiMMOY2bXAdf1uBhBEAQ7YMDkDPT4fe3wgyAI+pWZ5+7D4QdBELSN9WkffYpw+EEQBG1j2Axs488Kh68KlHZrLTjac7cNyXQ8sq8tE4NJm2fG0zYetlZbH55BhyRuvJqOQjjhqPcCh9zt2YmBpE1KaupltJyO5Fi1dL08cspKhySMHlKyTDmcTMmhjh107D8PA12MYNnNSJgp6jr8mcascPhBEATdph+/pE0RDj8IgqBNsgFQZl4TPxx+EATBNLBw+EEQBHOD6NIJgiCYA2QvbTvTwpe0kCwU/GF50u8D3gb8NjAOPAScbGYbmmy7GtgIVIFJM2scSGUH+i6WThAEwUzAHH9OzgauMrMXAy8lG/jpGuAwM3sJ8GPgEy22f52ZLU05e5gtLfxSGeaPtTSZN//ZZDL7OCInbt7iiKi5ZTRp44ksOZ6QZVZKaVmmJ58aaZttjgigC4e2Jm3K8gzknW6HeAbP9kSe9JRnaCAtB/RIej3Ha2tC9jvoGFjcI30dHkjLbCccx3xsOH3MSw7p5qRDPjwy7IioOZlOpxMYxmQHdPiSFgCvBk4CMLNxslb91QWzG4HjdjkzooUfBEHQPpZ16aQmYHF9oKZ8WtmQ0guAp4AvS/qhpHMlNbZe3wf829Ql4WpJtzZJeydmRws/CIKgyzi7bNYnuloqwMuBD5rZTZLOBk4H/hRA0hnAJHDhFNsfaWZrJe0FXCPpPjO7fqrMooUfBEHQJgbUsOTkYA2wxsxuyucvI7sBIOlE4M3Au20KDaiZrc3/PwlcDhzRKrNw+EEQBNOgEw7fzH4KPCbpkHzRcuAeSUcDpwHHmtnmZttKGpM0v/4beCNwV6v8oksnCIKgbToaPO2DwIWSBoGHgZOBm4Ehsm4agBvN7Pcl7Quca2YrgCXA5fn6CvBVM7uqVUbh8IMgCNrEBJNKq65caZndDjT2879oCtu1wIr898NkMk434fCDIAimgbOPvq+YFQ7fBgaoLtmvpc1u+zyVTGdoQ1pTvMARAnhJzaFr3zaUtElpiqu1tOa45NCZTzr01h6duUfzP+DQkY879nHFERraU+bBQYfG3qHtHnfsw3mjTbtid8wrcUw9ZRkaSuvVJxPfeHgZHUnXyZPXgONbB3NcVxOOc6cTZB06My+4Qt+9tJV0gKRvS7pX0t2SPtTrMgVBEDTSIZVOV+nHFv4k8FEzuy1/A32rpGvM7J5eFywIgqBOzfH03G/0ncM3s3XAuvz3Rkn3AvsB4fCDIOgLsg6dcPgdRdKBwMuAm5qsWwmsBHje3t3ptwuCIMgwqnRmmMhu0nd9+HUkzQP+BTjVzJ5pXG9m55jZMjNbtnhhX9+3giCYZRhZl05q6jf60lNKGiBz9hea2dd7XZ4gCIIdiS6djqDss7EvAfea2d95trHyANWFS1rajL3ovmQ6g08sTNrUJtK7bHJr6xC3ACNb07LMSiIcrDkkenKEfJ4cT3eJlRwySNe+6VBepbJDburIq+aRbo6m5bqpYwUwvjEdNrsy3DpssUeaaI5Qw2WHHLVWdYR8TpQXYGLTSDodxz72UBroXjeL0ZkPr7pJP3bpHAm8B3i9pNvzaUWvCxUEQVCn/tI29ddv9F0L38xuAMeIHEEQBD3DqJJ+Suo3+s7hB0EQ9DtZeOT+a8GnCIcfBEEwDWZiaIVw+EEQBG1j1GbgS9tw+EEQBG1iRAu/d5QHmNytdbTMgRftkUxmaI8N6bzG03d1m0xLIVVxyOsS51Pt545omaNpmZpL6rclfaqUxhxSv63pMnvQYPpis3FHhM9taemmKuljrqH0fm4cmbopHdDNmWMfd+q8UNkxqtO2dKU04jieE47yOGTIncGoWWda+JIWAucCh5HdS94H3A9cAhwIrAbeYWY/b7Lt0cDZQJlsYJQzW+XVj7LMIAiCPseoMZGcnJwNXGVmLyYb0OResoHMrzWzg4Fr8/kdkFQG/h44BjgUOEHSoa0yCocfBEHQJgbUrJacUkhaALya7GNTzGzczDYAbwG+kpt9BfidJpsfATxoZg+b2Thwcb7dlITDD4IgaBtzRMN39fG/AHgK+LKkH0o6Nx+QfEkeObgeQXivJtvuBzxWmF+TL5uScPhBEATtYmBWTU7AYkm3FKaVDSlVgJcDXzCzlwGbaNJ9MwXNXmq0fIkxO17aBkEQdJE24uGvN7PGAcqLrAHWmFk9BPxlZA7/CUn7mNk6SfsAT06x7QGF+f2Bta0KEy38IAiCaWBWS07pNOynwGOSDskXLScb7OlK4MR82YnAFU02vxk4WNJBkgaB4/PtpmRWtPCtVMFGFre0GT/45cl0NJmO/Fd+didl1E7UBoeTNqVxR3TA2q7LvmqONOQ4MVG6bVAdTgsP5ai3tqUHxrahdORJD6UJx3EopWWO5tg/qjoG6i53YDCfSjpaq23ZmLYZmZ/Oa9umdDoD6evBPOepZ/85jhX8yGGTzImadSyWzgeBC3On/TBwMllj/GuS3g88CrwdQNK+ZPLLFWY2KekU4FtksszzzOzuVhnNCocfBEHQXaxjH16Z2e1As26f5U1s1wIrCvOrgFXevMLhB0EQtIlB/aXsjCIcfhAEQduYq4++3wiHHwRBMA0ilk4QBMFcwIyadW84xU4RDj8IgqBNog8/CIJgzpCNeTXT6EuH327IT6lCaWjPlmmWDzw4ma/nEa1T9/RJR15Dg7vvcj5btrT88A6AcmVe0qY6sSFpMzi0JGkzWU3rtqXOnJYlRzqeYLqVSlrzv238Z46UHHmVW3/L4GlVToyvT9qMjD4vaTM+8UzSpjr5bNLGdX450hkYWJi0maym04GPOGzSzMSXtn33pe10Qn4GQRB0l44FT+sqfefwmUbIzyAIgu5Tc0z9RT926TQL+fmfGo3yqHMrAQ44YGFXChYEQZBh2AxU6fRjC98V8tPMzjGzZWa2bPFi1+BxQRAEHSRa+J2g7ZCfQRAEXce6NX5u5+jHFn7bIT+DIAi6i7n++g1ZH96lJK0AzmJ7yM+/Stg/BTwCLAbSmrSZR9RrZhH16m+eb2atddwJJF1Ftj9SrDezo3clr07Slw5/uki6JTG6zIwk6jWziHoF/Uo/dukEQRAEzwHh8IMgCOYIs83hn9PrAjxHRL1mFlGvoC+ZVX34QRAEwdTMthZ+EARBMAXh8IMgCOYIM87hSzpa0v2SHpR0epP1kvS5fP2dkl7ei3K2i6Ne787rc6ek70t6aS/KOR1SdSvY/YakqqTjulm+6eKpl6TXSrpd0t2SvtPtMk4Hx7m4m6RvSLojr9fJvShnMA3MbMZMZB9iPQS8ABgE7gAObbBZAfwbWUyeVwA39brcHarXbwKL8t/HzIR6eetWsPsPYBVwXK/L3aFjthC4B3hePr9Xr8vdoXr9d+Bv8t97Aj8DBntd9pjS00xr4XtCJ78FuMAybgQWStqn2wVtk2S9zOz7ZvbzfPZGshhDMwFvuOsPAv8CPNnNwu0Cnnq9C/i6mT0KYGYzoW6eehkwX5KAeWQOf+aFjpyDzDSH3yx08n7TsOk32i3z+8meYmYCybpJ2g94K/CPXSzXruI5Zr8CLJJ0naRbJb23a6WbPp56fR74VbKghj8CPmQzcfinOUg/RstshSd0siu8cp/hLrOk15E5/N96TkvUOTx1Ows4zcyqWaNxRuCpVwU4HFgOjAD/T9KNZvbj57pwu4CnXm8CbgdeD7wQuEbSd80sPSZi0FNmmsP3hE6eieGVXWWW9BLgXOAYM3u6S2XbVTx1WwZcnDv7xcAKSZNm9n+7UsLp4T0X15vZJmCTpOuBlwL97PA99ToZONPMDHhQ0k+AFwM/6E4Rg+ky07p0PKGTrwTem6t1XgH8wszWdbugbZKsl6TnAV8H3tPnLcRGknUzs4PM7EAzOxC4DPhvfe7swXcuXgG8SlJF0ijZyG33drmc7eKp16NkTy1IWgIcAjzc1VIG02JGtfDNbFLSKcC32B46+W5Jv5+v/0cylccK4EFgM1lrpK9x1uvPgD2Af8hbwpM2AyIXOus24/DUy8zuzcPo3kk2/NG5ZnZX70qdxnm8/hI4X9KPyLqATjOz2RA2edYToRWCIAjmCDOtSycIgiCYJuHwgyAI5gjh8IMgCOYI4fCDIAjmCOHwgyAI5gjh8IMgCOYI4fCDIAjmCOHwgyAI5gjh8INZhaTDJV0raUs+gMerJb1D0vd6XbYg6DXh8INZg6TfAL4LfBt4Cdm4AX8OnAH8aQ+LFgR9QYRWCGYNeTTKdWb2znx+BfAN4Hoze11PCxcEfcCMCp4WBFMhaW/gVUDRsY+TPcVG6z4IiC6dYPbwq/n/mwvLDgHuN7MbelCeIOg7wuEHs4WFZCMz1QAkzSfru9/cwzIFQV8RDj+YLdxOFpv9E5IOAS4E1gEvlHRwLwsWBP1COPxgVmBmPyFr0f8BcAewEXgDcBfw/R4WLQj6hlDpBEEQzBGihR8EQTBHCIcfBEEwRwiHHwRBMEcIhx8EQTBHCIcfBEEwRwiHHwRBMEcIhx8EQTBHCIcfBEEwR/j/sEKkhaKgzPUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Plot Heat Map of average number of aversive stimuli received\n",
    "plt.pcolormesh(alphas_hm,betas_hm,o_heatmap,cmap=\"inferno\")\n",
    "plt.title(\"Average number of aversive outcomes\",fontsize=14,**font)\n",
    "plt.xlabel(r'$\\alpha$',fontsize=14,**font);\n",
    "plt.ylabel(r'$\\beta$',fontsize=14,**font); \n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "loaded-metabolism",
   "metadata": {},
   "source": [
    "## Task (d): Likelihood function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "hazardous-dictionary",
   "metadata": {},
   "outputs": [],
   "source": [
    "def model_neg_log_likelihood(theta,p,choices,outcomes,V_0):\n",
    "    \n",
    "    alpha = theta[0]\n",
    "    beta = theta[1]\n",
    "    \n",
    "    V = np.array([V_0,V_0])\n",
    "\n",
    "    choice_probabilities = np.zeros(trials)\n",
    "    \n",
    "    for t in range(trials):\n",
    "        \n",
    "        c = choices.loc[p,t]\n",
    "        o = outcomes.loc[p,t]\n",
    "        \n",
    "        if c == 1:\n",
    "            \n",
    "            c_alt = 2\n",
    "        \n",
    "        else:\n",
    "            \n",
    "            c_alt = 1\n",
    "        \n",
    "        choice_probabilities[t] = 1/(1 + np.exp(beta*(V[c-1]-V[c_alt-1])))\n",
    "        \n",
    "        V[c-1] = np.copy(V[c-1]+ alpha*(o - V[c-1]))\n",
    "        \n",
    "    return -np.sum(np.log(choice_probabilities))\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "separated-bicycle",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "NLL for the second participant is: 64.24159844691494\n"
     ]
    }
   ],
   "source": [
    "#Check NLL function with second participant\n",
    "theta = np.array([0.3,8])\n",
    "print(\"NLL for the second participant is: \" + str(model_neg_log_likelihood(theta,1,choices,outcomes,0.5)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "complimentary-modeling",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "NLL for the first participant is: 50.19065076029976\n",
      "NLL for the 10th participant is: 58.602608072173666\n"
     ]
    }
   ],
   "source": [
    "#NLL for the first and 10th participant using given parameters.\n",
    "print(\"NLL for the first participant is: \" + str(model_neg_log_likelihood(theta,0,choices,outcomes,0.5)))\n",
    "print(\"NLL for the 10th participant is: \" + str(model_neg_log_likelihood(theta,9,choices,outcomes,0.5)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "moved-parish",
   "metadata": {},
   "source": [
    "## Task (e): Model fitting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "neural-roots",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 50/50 [00:12<00:00,  3.91it/s]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mean of the fitted alpha is: 0.42374345533863056\n",
      "The variance of the fitted alpha is: 0.014278285594727625\n",
      "The mean of the fitted beta is: 5.2789636097567465\n",
      "The variance of the fitted beta is: 3.0381890388988757\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "#Find optimized values\n",
    "optimized_alphas = np.zeros(50)\n",
    "optimized_betas = np.zeros(50)\n",
    "\n",
    "theta_guess = np.array([0.3,8])\n",
    "\n",
    "for i in tqdm(range(50)):\n",
    "    optimized_params = sp.optimize.minimize(model_neg_log_likelihood, theta_guess, args=(i,choices, outcomes,0.5), method='Nelder-Mead').x\n",
    "    optimized_alphas[i] = optimized_params[0]\n",
    "    optimized_betas[i] = optimized_params[1] \n",
    "    \n",
    "mean_optimized_alphas = np.average(optimized_alphas)\n",
    "var_optimized_alphas = np.std(optimized_alphas)**2\n",
    "mean_optimized_betas = np.average(optimized_betas)\n",
    "var_optimized_betas = np.std(optimized_betas)**2\n",
    "\n",
    "print(\"The mean of the fitted alpha is: \" + str(mean_optimized_alphas))\n",
    "print(\"The variance of the fitted alpha is: \" + str(var_optimized_alphas))\n",
    "print(\"The mean of the fitted beta is: \" + str(mean_optimized_betas))\n",
    "print(\"The variance of the fitted beta is: \" + str(var_optimized_betas))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "fleet-rachel",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[47.75940023 54.91954282 34.59878631 27.74201802 56.98302465 57.05618112\n",
      " 45.11195183 54.81692477 49.62291447 47.85597346 47.56697524 34.73100298\n",
      " 44.5429264  50.79311437 62.4647707  54.72651213 30.8777312  31.10233063\n",
      " 66.41251742 45.91596442 56.65855605 47.46280706 63.65265147 40.22606036\n",
      " 97.30860193 67.91003084 63.09078768 88.13828263 74.39358922 54.77487413\n",
      " 55.45645263 70.11715787 73.23142126 68.70085192 78.63913526 83.57885404\n",
      " 59.01812645 52.3950467  98.90208895 87.56975594 56.76813896 61.83659952\n",
      " 62.4290714  84.3365027  38.99229342 82.72018845 59.85036959 32.57472408\n",
      " 83.25344974 45.63032546]\n"
     ]
    }
   ],
   "source": [
    "#Find nll values for each participant for model 1\n",
    "nll_model1 = np.zeros(50)\n",
    "for i in range(50):\n",
    "    theta_nll1 = np.array([optimized_alphas[i],optimized_betas[i]])\n",
    "    nll_model1[i] = model_neg_log_likelihood(theta_nll1,i,choices, outcomes,0.5)\n",
    "print(nll_model1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "applicable-queen",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Plot Model fitting\n",
    "\n",
    "plt.scatter(np.linspace(1,25,25),optimized_alphas[:25], color = 'red', label = \"Anxious\")\n",
    "plt.scatter(np.linspace(26,50,25),optimized_alphas[25:], color = 'green',label = \"Control\")\n",
    "plt.title(\"Fitted learning rate \" r'$\\alpha$',fontsize=20,**font)\n",
    "plt.xlabel(\"Participant index\",fontsize=20,**font)\n",
    "plt.ylabel(\"Parameter value\",fontsize=20,**font)\n",
    "plt.axhline(y = 0.4237 + np.sqrt(0.0143),linestyle = ':')\n",
    "plt.axhline(y = 0.4237,linestyle = '-')\n",
    "plt.axhline(y = 0.4237 - np.sqrt(0.0143),linestyle = ':')\n",
    "plt.tick_params(axis='both', which='major', labelsize=15)\n",
    "plt.legend(fontsize=13,loc = 'upper right').get_frame().set_linewidth(1.5)\n",
    "plt.show()\n",
    "\n",
    "plt.scatter(np.linspace(1,25,25),optimized_betas[:25], color = 'red',label = \"Anxious\")\n",
    "plt.scatter(np.linspace(26,50,25),optimized_betas[25:], color = 'green',label = \"Control\")\n",
    "plt.title(\"Fitted inverse temperature \" r'$\\beta$',fontsize=20,**font)\n",
    "plt.xlabel(\"Participant index\",fontsize=20,**font)\n",
    "plt.ylabel(\"Parameter value\",fontsize=20,**font)\n",
    "plt.axhline(y = 5.2790 + np.sqrt(3.0382),linestyle = ':')\n",
    "plt.axhline(y = 5.2790,linestyle = '-')\n",
    "plt.axhline(y = 5.2790 - np.sqrt(3.0382),linestyle = ':')\n",
    "plt.legend(fontsize=13).get_frame().set_linewidth(1.5)\n",
    "plt.tick_params(axis='both', which='major', labelsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "little-section",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson´s correlation coefficient between estimated parameters across all participants is: 0.07219200521010426\n"
     ]
    }
   ],
   "source": [
    "#Calculate Pearson´s correlation coefficient between estimated parameters across all participants\n",
    "\n",
    "pearsons_corr_all, p_val_all = sp.stats.pearsonr(optimized_alphas, optimized_betas)\n",
    "\n",
    "print(\"The Pearson´s correlation coefficient between estimated parameters across all participants is: \" + str(pearsons_corr_all))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "complex-section",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson´s correlation coefficient between estimated parameters for the control group is: -0.10274632925287824\n",
      "The Pearson´s correlation coefficient between estimated parameters for the high anxious group is: -0.13327926387630962\n"
     ]
    }
   ],
   "source": [
    "#Calculate Pearson´s correlation coefficient between estimated parameters for participants within each group\n",
    "\n",
    "pearsons_corr_control, p_val_control = sp.stats.pearsonr(optimized_alphas[25:], optimized_betas[25:])\n",
    "pearsons_corr_anxious, p_val_anxious = sp.stats.pearsonr(optimized_alphas[:25], optimized_betas[:25])\n",
    "\n",
    "\n",
    "print(\"The Pearson´s correlation coefficient between estimated parameters for the control group is: \" + str(pearsons_corr_control))\n",
    "print(\"The Pearson´s correlation coefficient between estimated parameters for the high anxious group is: \" + str(pearsons_corr_anxious))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "increased-aberdeen",
   "metadata": {},
   "source": [
    "## Task (f): Group comparison"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "aging-forestry",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The variance of optimized alphas for anxious group is: 0.008999820068125988\n",
      "The variance of optimized alphas for control group is: 0.015108006780675053\n",
      "The variance of optimized betas for anxious group is: 2.0866320446041646\n",
      "The variance of optimized betas for control group is: 2.439743557475143\n",
      "Ttest_indResult(statistic=3.033285774110115, pvalue=0.003978909213480201)\n",
      "Ttest_indResult(statistic=3.303459937159372, pvalue=0.0018626518919232415)\n"
     ]
    }
   ],
   "source": [
    "#Check if variances are similar\n",
    "print(\"The variance of optimized alphas for anxious group is: \" + str(np.var(optimized_alphas[24:])))\n",
    "print(\"The variance of optimized alphas for control group is: \" + str(np.var(optimized_alphas[:24])))\n",
    "print(\"The variance of optimized betas for anxious group is: \" + str(np.var(optimized_betas[24:])))\n",
    "print(\"The variance of optimized betas for control group is: \" + str(np.var(optimized_betas[:24])))\n",
    "\n",
    "# Welsch t-test\n",
    "print(stats.ttest_ind(optimized_alphas[:25],optimized_alphas[25:] , equal_var=False))\n",
    "print(stats.ttest_ind(optimized_betas[:25],optimized_betas[25:] , equal_var=False))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "endangered-unknown",
   "metadata": {},
   "source": [
    "## Task (g): Parameter recovery"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "collaborative-accident",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Use suggested variance, covariances are set to 0\n",
    "cov = np.array([[0.01,0],[0,0.5]])\n",
    "#For mean, use mean of the fitted parameter values obtained in task e\n",
    "mean_fitted = np.array([0.4237,5.2790])\n",
    "#Draw sampled parameters\n",
    "sampled_parameters = np.random.multivariate_normal(mean_fitted,cov,50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "serial-bunny",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Plot sampled parameters\n",
    "plt.scatter(np.linspace(1,50,50),sampled_parameters[:,0], color = 'blue')\n",
    "plt.title(\"Sampled learning rates \" r'$\\alpha$',fontsize=20,**font)\n",
    "plt.xlabel(\"Sampled parameter index\",fontsize=20,**font)\n",
    "plt.ylabel(\"Parameter value\",fontsize=20,**font)\n",
    "plt.axhline(y = 0.4237 + np.sqrt(0.0143),linestyle = ':')\n",
    "plt.axhline(y = 0.4237,linestyle = '-')\n",
    "plt.axhline(y = 0.4237 - np.sqrt(0.0143),linestyle = ':')\n",
    "plt.tick_params(axis='both', which='major', labelsize=15)\n",
    "plt.show()\n",
    "\n",
    "plt.scatter(np.linspace(1,50,50),sampled_parameters[:,1], color = 'yellow')\n",
    "plt.title(\"Sampled inverse temperature \" r'$\\beta$',fontsize=20,**font)\n",
    "plt.xlabel(\"Sampled parameter index\",fontsize=20,**font)\n",
    "plt.ylabel(\"Parameter value\",fontsize=20,**font)\n",
    "plt.axhline(y = 5.2790 + np.sqrt(3.0382),linestyle = ':')\n",
    "plt.axhline(y = 5.2790,linestyle = '-')\n",
    "plt.axhline(y = 5.2790 - np.sqrt(3.0382),linestyle = ':')\n",
    "plt.tick_params(axis='both', which='major', labelsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "legislative-microphone",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Identify nonsensical values and resamples.\n",
    "for i in range (len(sampled_parameters[:,0])):\n",
    "    if sampled_parameters[i,0] > (0.4237 + np.sqrt(0.0143)) or sampled_parameters[i,0] < (0.4237 - np.sqrt(0.0143)):\n",
    "        \n",
    "        new_samp = np.random.multivariate_normal(mean_fitted,cov)[0]\n",
    "        while new_samp >  (0.4237 + np.sqrt(0.0143)) or new_samp < (0.4237 - np.sqrt(0.0143)):\n",
    "            new_samp = np.random.multivariate_normal(mean_fitted,cov)[0]\n",
    "        sampled_parameters[i,0] = new_samp\n",
    "\n",
    "for i in range (len(sampled_parameters[:,1])):\n",
    "    if sampled_parameters[i,1] > (5.2790 + np.sqrt(3.0382)) or sampled_parameters[i,1] < (5.2790 - np.sqrt(3.0382)):\n",
    "        \n",
    "        new_samp = np.random.multivariate_normal(mean_fitted,cov)[1]\n",
    "        while new_samp >  (5.2790 + np.sqrt(3.0382)) or new_samp < (5.2790 - np.sqrt(3.0382)):\n",
    "            new_samp = np.random.multivariate_normal(mean_fitted,cov)[1]\n",
    "        sampled_parameters[i,1] = new_samp\n",
    "\n",
    "#Plotting samples parameters after identifying outliers and resampling\n",
    "plt.scatter(np.linspace(1,50,50),sampled_parameters[:,0], color = 'blue')\n",
    "plt.title(\"Sampled learning rates \" r'$\\alpha$',fontsize=20,**font)\n",
    "plt.xlabel(\"Sampled parameter index\",fontsize=20,**font)\n",
    "plt.ylabel(\"Parameter value\",fontsize=20,**font)\n",
    "plt.axhline(y = 0.4237 + np.sqrt(0.0143),linestyle = ':')\n",
    "plt.axhline(y = 0.4237,linestyle = '-')\n",
    "plt.axhline(y = 0.4237 - np.sqrt(0.0143),linestyle = ':')\n",
    "plt.tick_params(axis='both', which='major', labelsize=15)\n",
    "plt.show()\n",
    "\n",
    "plt.scatter(np.linspace(1,50,50),sampled_parameters[:,1], color = 'yellow')\n",
    "plt.title(\"Sampled inverse temperature \" r'$\\beta$',fontsize=20,**font)\n",
    "plt.xlabel(\"Sampled parameter index\",fontsize=20,**font)\n",
    "plt.ylabel(\"Parameter value\",fontsize=20,**font)\n",
    "plt.axhline(y = 5.2790 + np.sqrt(3.0382),linestyle = ':')\n",
    "plt.axhline(y = 5.2790,linestyle = '-')\n",
    "plt.axhline(y = 5.2790 - np.sqrt(3.0382),linestyle = ':')\n",
    "plt.tick_params(axis='both', which='major', labelsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "physical-begin",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 50/50 [00:00<00:00, 906.70it/s]\n"
     ]
    }
   ],
   "source": [
    "#Used Sampled values to simulate 50 sets of data\n",
    "\n",
    "simulated_choices = np.zeros((50,160))\n",
    "simulated_outcomes = np.zeros((50,160))\n",
    "simulated_V_a = np.zeros((50,160))\n",
    "simulated_V_b = np.zeros((50,160))\n",
    "\n",
    "for i in tqdm(range(50)):\n",
    "    \n",
    "   \n",
    "    simulated_choices[i,:] , simulated_outcomes[i,:] , simulated_V_a[i,:] ,simulated_V_b[i,:] = model_simulate(sampled_parameters[i,0], sampled_parameters[i,1], 0.5)\n",
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "wrapped-liechtenstein",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 50/50 [00:05<00:00,  9.31it/s]\n"
     ]
    }
   ],
   "source": [
    "#Fit parameter values to simulated data sets\n",
    "\n",
    "def model_neg_log_likelihood_taskg(theta,choices,outcomes,V_0,trials):\n",
    "    \n",
    "    alpha = theta[0]\n",
    "    beta = theta[1]\n",
    "    \n",
    "    V = np.array([V_0,V_0])\n",
    "\n",
    "    choice_probabilities = np.zeros(trials)\n",
    "    \n",
    "    for t in range(trials):\n",
    "        \n",
    "        c = int(choices[t])\n",
    "        o = outcomes[t]\n",
    "        \n",
    "        if c == 1:\n",
    "            \n",
    "            c_alt = 2\n",
    "        \n",
    "        else:\n",
    "            \n",
    "            c_alt = 1\n",
    "        \n",
    "        choice_probabilities[t] = 1/(1 + np.exp(beta*(V[c-1]-V[c_alt-1])))\n",
    "        \n",
    "        V[c-1] = np.copy(V[c-1]+ alpha*(o - V[c-1]))\n",
    "        \n",
    "    return -np.sum(np.log(choice_probabilities))\n",
    "\n",
    "\n",
    "\n",
    "optimized_alphas_taskg = np.zeros(50)\n",
    "optimized_betas_taskg = np.zeros(50)\n",
    "\n",
    "#set starting parameters\n",
    "theta_guess = np.array([0.3,8])\n",
    "\n",
    "for i in tqdm(range(50)):\n",
    "    optimized_alphas_taskg[i] = sp.optimize.minimize(model_neg_log_likelihood_taskg, theta_guess, args=(simulated_choices[i,:], simulated_outcomes[i,:] ,0.5,160), method='Nelder-Mead').x[0]\n",
    "    optimized_betas_taskg[i] = sp.optimize.minimize(model_neg_log_likelihood_taskg, theta_guess, args=(simulated_choices[i,:], simulated_outcomes[i,:] ,0.5,160), method='Nelder-Mead').x[1]\n",
    " \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "coupled-administrator",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.6079995473899185\n",
      "0.56036023224783\n"
     ]
    }
   ],
   "source": [
    "#Calculate and illustrate Pearson´s correlation between parameter values used to simulate the data, and the parameter values obtained from fitting the model to the simulated data\n",
    "pearsons_corr_sim_alpha , p_val_sim_alpha = sp.stats.pearsonr(sampled_parameters[:,0], optimized_alphas_taskg)\n",
    "pearsons_corr_sim_beta , p_val_sim_beta = sp.stats.pearsonr(sampled_parameters[:,1], optimized_betas_taskg)\n",
    "\n",
    "print(pearsons_corr_sim_alpha)\n",
    "print(pearsons_corr_sim_beta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "designed-sellers",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Illustration Parameter Recovery\n",
    "\n",
    "plt.scatter(sampled_parameters[:,0],optimized_alphas_taskg, color=\"none\", edgecolor=\"blue\")\n",
    "plt.axline((0.45, 0.45), slope = 1, color='blue')\n",
    "plt.title(\"Sampled versus new fitted learning rates\",fontsize=16,**font)\n",
    "plt.xlabel(\"Sampled \" r'$\\alpha$',fontsize=16,**font)\n",
    "plt.ylabel(\"Fitted \" r'$\\alpha$',fontsize=16,**font)\n",
    "plt.tick_params(axis='both', which='major', labelsize=14)\n",
    "plt.show()\n",
    "\n",
    "plt.scatter(sampled_parameters[:,1],optimized_betas_taskg, color=\"none\", edgecolor=\"red\")\n",
    "plt.axline((5, 5), slope = 1, color='red')\n",
    "plt.title(\"Sampled versus new fitted inverse temperature\",fontsize=16,**font)\n",
    "plt.xlabel(\"Sampled \" r'$\\beta$',fontsize=16,**font)\n",
    "plt.ylabel(\"Fitted \" r'$\\beta$',fontsize=16,**font)\n",
    "plt.tick_params(axis='both', which='major', labelsize=14)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "flying-oliver",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 5/5 [00:13<00:00,  2.63s/it]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.5265266  0.64601317 0.61179113 0.6496717  0.29247156]\n",
      "[0.59279444 0.60921686 0.5506945  0.52448613 0.48381727]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "#Repeat process 5 times\n",
    "\n",
    "optimized_alphas_taskg = np.zeros((5,50))\n",
    "optimized_betas_taskg = np.zeros((5,50))\n",
    "\n",
    "pearsons_correlations_alphas =  np.zeros(5)\n",
    "pearsons_correlations_betas =  np.zeros(5)\n",
    "\n",
    "for j in tqdm(range(5)):\n",
    "    \n",
    "    sampled_parameters = np.random.multivariate_normal(mean_fitted,cov,50)\n",
    "    \n",
    "    for i in range (len(sampled_parameters[:,0])):\n",
    "        if sampled_parameters[i,0] > (0.4237 + np.sqrt(0.0143)) or sampled_parameters[i,0] < (0.4237 - np.sqrt(0.0143)):\n",
    "            new_samp = np.random.multivariate_normal(mean_fitted,cov)[0]\n",
    "            while new_samp >  (0.4237 + np.sqrt(0.0143)) or new_samp < (0.4237 - np.sqrt(0.0143)):\n",
    "                new_samp = np.random.multivariate_normal(mean_fitted,cov)[0]\n",
    "            sampled_parameters[i,0] = new_samp\n",
    "\n",
    "    for i in range (len(sampled_parameters[:,1])):\n",
    "        if sampled_parameters[i,1] > (5.2790 + np.sqrt(3.0382)) or sampled_parameters[i,1] < (5.2790 - np.sqrt(3.0382)):\n",
    "\n",
    "            new_samp = np.random.multivariate_normal(mean_fitted,cov)[1]\n",
    "            while new_samp >  (5.2790 + np.sqrt(3.0382)) or new_samp < (5.2790 - np.sqrt(3.0382)):\n",
    "                new_samp = np.random.multivariate_normal(mean_fitted,cov)[1]\n",
    "            sampled_parameters[i,1] = new_samp\n",
    "    \n",
    "    \n",
    "    for i in range(50):\n",
    "        \n",
    "        sim_cho = np.zeros(160)\n",
    "        sim_out = np.zeros(160)\n",
    "        sim_V_a = np.zeros(160)\n",
    "        sim_V_b = np.zeros(160)\n",
    "   \n",
    "        theta_guess = np.array([0.3,8])\n",
    "        \n",
    "        sim_cho , sim_out, sim_V_a ,sim_V_b = model_simulate(sampled_parameters[i,0], sampled_parameters[i,1], 0.5)\n",
    "        optimization = sp.optimize.minimize(model_neg_log_likelihood_taskg, theta_guess, args=(sim_cho, sim_out ,0.5,160), method='Nelder-Mead').x\n",
    "        optimized_alphas_taskg[j,i] = optimization[0]\n",
    "        optimized_betas_taskg[j,i] = optimization[1]\n",
    "        \n",
    "\n",
    "    pearsons_correlations_alphas[j] , p_val_alpha = sp.stats.pearsonr(sampled_parameters[:,0], optimized_alphas_taskg[j,:])\n",
    "    \n",
    "    pearsons_correlations_betas[j] , p_val_beta = sp.stats.pearsonr(sampled_parameters[:,1], optimized_betas_taskg[j,:])\n",
    "\n",
    "print(pearsons_correlations_alphas)\n",
    "print(pearsons_correlations_betas)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "romance-freeware",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of trials: 160\n",
      "Number of simulated data sets: 100\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 5/5 [00:52<00:00, 10.46s/it]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.6419085  0.5197364  0.54053194 0.47097167 0.6177558 ]\n",
      "[0.5869481  0.62171688 0.57918867 0.65350645 0.49418883]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "#Explore how number of trials and number of simulated data sets affects performance of the parameter recovery\n",
    "\n",
    "trials_taskg = int(input(\"Number of trials: \"))\n",
    "sim_sets = int(input(\"Number of simulated data sets: \"))\n",
    "\n",
    "def model_simulate_taskg(alpha, beta, V_0):  \n",
    "    \n",
    "    c = np.zeros(trials_taskg)\n",
    "    o = np.zeros(trials_taskg)\n",
    "    V_a = np.zeros(trials_taskg)\n",
    "    V_b = np.zeros(trials_taskg)\n",
    "    \n",
    "    #Initial conditions\n",
    "    V_a[0] = V_0\n",
    "    V_b[0] = V_0\n",
    "    \n",
    "    #First 40 trial set\n",
    "    for t in range(0,int(trials_taskg/4)):\n",
    "        \n",
    "        #Probability of choosing A\n",
    "        p_choose_A = 1/(1 + np.exp(beta*(V_a[t]-V_b[t])))\n",
    "        \n",
    "        #If A is chosen\n",
    "        if np.random.rand() < p_choose_A:\n",
    "            \n",
    "            c[t] = 1 \n",
    "            \n",
    "            #Will give aversive outcome with p = 0.6\n",
    "            if np.random.rand() < 0.6:\n",
    "                \n",
    "                o[t] = 1\n",
    "            \n",
    "            #Update V_a but not V_b\n",
    "            V_a[t+1] =  np.copy(V_a[t] + alpha*(o[t] - V_a[t]))\n",
    "            V_b[t+1] =  np.copy(V_b[t]) \n",
    "        \n",
    "        #If B is chosen\n",
    "        else:\n",
    "            \n",
    "            c[t] = 2\n",
    "            \n",
    "            #Will give aversive outcome with p = 0.4\n",
    "            if np.random.rand() < 0.4:\n",
    "                \n",
    "                o[t] = 1\n",
    "        \n",
    "            #Update V_b but not V_a\n",
    "            V_a[t+1] =  np.copy(V_a[t]) \n",
    "            V_b[t+1] =  np.copy(V_b[t] + alpha*(o[t] - V_b[t]))\n",
    "                \n",
    "    #Second 40 trial set\n",
    "    for t in range(int(trials_taskg/4),int(trials_taskg/2)):\n",
    "        \n",
    "        #Probability of choosing A\n",
    "        p_choose_A = 1/(1 + np.exp(beta*(V_a[t]-V_b[t])))\n",
    "        \n",
    "        if np.random.rand() < p_choose_A:\n",
    "            \n",
    "            c[t] = 1\n",
    "            \n",
    "            if np.random.rand() < 0.8:\n",
    "            \n",
    "                o[t] = 1\n",
    "            \n",
    "            V_a[t+1] =  np.copy(V_a[t] + alpha*(o[t] - V_a[t]))\n",
    "            V_b[t+1] =  np.copy(V_b[t]) \n",
    "            \n",
    "        else:\n",
    "            \n",
    "            c[t] = 2\n",
    "            \n",
    "            if np.random.rand() < 0.2:\n",
    "                \n",
    "                o[t] = 1\n",
    "        \n",
    "            V_a[t+1] =  np.copy(V_a[t]) \n",
    "            V_b[t+1] =  np.copy(V_b[t] + alpha*(o[t] - V_b[t]))\n",
    "                \n",
    "    #Third 40 trial set        \n",
    "    for t in range(int(trials_taskg/2),int((3*trials_taskg)/4)):\n",
    "        \n",
    "        p_choose_A = 1/(1 + np.exp(beta*(V_a[t]-V_b[t])))\n",
    "        \n",
    "        if np.random.rand() < p_choose_A:\n",
    "            \n",
    "            c[t] = 1\n",
    "            \n",
    "            if np.random.rand() < 0.6:\n",
    "                \n",
    "                o[t] = 1\n",
    "            \n",
    "            V_a[t+1] =  np.copy(V_a[t] + alpha*(o[t] - V_a[t]))\n",
    "            V_b[t+1] =  np.copy(V_b[t])\n",
    "            \n",
    "        else:\n",
    "            \n",
    "            c[t] = 2\n",
    "            \n",
    "            if np.random.rand() < 0.4:\n",
    "            \n",
    "                o[t] = 1\n",
    "        \n",
    "            V_a[t+1] =  np.copy(V_a[t]) \n",
    "            V_b[t+1] =  np.copy(V_b[t] + alpha*(o[t] - V_b[t]))     \n",
    "    \n",
    "    #Fourth 40 trial set         \n",
    "    for t in range(int((3*trials_taskg)/4),trials_taskg-1):\n",
    "        \n",
    "        p_choose_A = 1/(1 + np.exp(beta*(V_a[t]-V_b[t])))\n",
    "        \n",
    "        if np.random.rand() < p_choose_A:\n",
    "            \n",
    "            c[t] = 1\n",
    "            \n",
    "            if np.random.rand() < 0.65:\n",
    "                \n",
    "                o[t] = 1\n",
    "            \n",
    "            V_a[t+1] =  np.copy(V_a[t] + alpha*(o[t] - V_a[t]))\n",
    "            V_b[t+1] =  np.copy(V_b[t])\n",
    "            \n",
    "        else:\n",
    "            \n",
    "            c[t] = 2\n",
    "            \n",
    "            if np.random.rand() < 0.35:\n",
    "                \n",
    "                o[t] = 1\n",
    "\n",
    "            V_a[t+1] =  np.copy(V_a[t]) \n",
    "            V_b[t+1] =  np.copy(V_b[t] + alpha*(o[t] - V_b[t]))     \n",
    "    \n",
    "    #Last trial\n",
    "    p_choose_A = 1/(1 + np.exp(beta*(V_a[trials_taskg-1]-V_b[trials_taskg-1])))\n",
    "    \n",
    "    if np.random.rand() < p_choose_A:\n",
    "            \n",
    "        c[trials_taskg-1] = 1\n",
    "            \n",
    "        if np.random.rand() < 0.65:\n",
    "                \n",
    "            o[trials_taskg-1] = 1\n",
    "    else:\n",
    "            \n",
    "        c[trials_taskg-1] = 2\n",
    "            \n",
    "        if np.random.rand() < 0.35:\n",
    "                \n",
    "            o[trials_taskg-1] = 1\n",
    "    \n",
    "    return c, o, V_a, V_b\n",
    "\n",
    "\n",
    "\n",
    "optimized_alphas_taskg = np.zeros((5,sim_sets))\n",
    "optimized_betas_taskg = np.zeros((5,sim_sets))\n",
    "\n",
    "pearsons_correlations_alphas =  np.zeros(5)\n",
    "pearsons_correlations_betas =  np.zeros(5)\n",
    "\n",
    "for j in tqdm(range(5)):\n",
    "    \n",
    "    sampled_parameters = np.random.multivariate_normal(mean_fitted,cov,sim_sets)\n",
    "   \n",
    "    for i in range (len(sampled_parameters[:,0])):\n",
    "        if sampled_parameters[i,0] > (0.4237 + np.sqrt(0.0143)) or sampled_parameters[i,0] < (0.4237 - np.sqrt(0.0143)):\n",
    "            new_samp = np.random.multivariate_normal(mean_fitted,cov)[0]\n",
    "            while new_samp >  (0.4237 + np.sqrt(0.0143)) or new_samp < (0.4237 - np.sqrt(0.0143)):\n",
    "                new_samp = np.random.multivariate_normal(mean_fitted,cov)[0]\n",
    "            sampled_parameters[i,0] = new_samp\n",
    "\n",
    "    for i in range (len(sampled_parameters[:,1])):\n",
    "        if sampled_parameters[i,1] > (5.2790 + np.sqrt(3.0382)) or sampled_parameters[i,1] < (5.2790 - np.sqrt(3.0382)):\n",
    "\n",
    "            new_samp = np.random.multivariate_normal(mean_fitted,cov)[1]\n",
    "            while new_samp >  (5.2790 + np.sqrt(3.0382)) or new_samp < (5.2790 - np.sqrt(3.0382)):\n",
    "                new_samp = np.random.multivariate_normal(mean_fitted,cov)[1]\n",
    "            sampled_parameters[i,1] = new_samp\n",
    "    \n",
    "    \n",
    "    simulated_choices = np.zeros((sim_sets,trials_taskg))\n",
    "    simulated_outcomes = np.zeros((sim_sets,trials_taskg))\n",
    "    simulated_V_a = np.zeros((sim_sets,trials_taskg))\n",
    "    simulated_V_b = np.zeros((sim_sets,trials_taskg))\n",
    "\n",
    "    for i in range(sim_sets):\n",
    "        simulated_choices[i,:] , simulated_outcomes[i,:] , simulated_V_a[i,:] , simulated_V_b[i,:] = model_simulate_taskg(sampled_parameters[i,0], sampled_parameters[i,1], 0.5)\n",
    " \n",
    "    #set starting parameters\n",
    "    theta_guess = np.array([0.3,8])\n",
    "\n",
    "    for i in range(sim_sets):\n",
    "        optimized_alphas_taskg[j,i] = sp.optimize.minimize(model_neg_log_likelihood_taskg, theta_guess, args=(simulated_choices[i,:], simulated_outcomes[i,:] ,0.5,trials_taskg), method='Nelder-Mead').x[0]\n",
    "        optimized_betas_taskg[j,i] = sp.optimize.minimize(model_neg_log_likelihood_taskg, theta_guess, args=(simulated_choices[i,:], simulated_outcomes[i,:] ,0.5,trials_taskg), method='Nelder-Mead').x[1]\n",
    "   \n",
    "    pearsons_correlations_alphas[j] , p_val_alpha = sp.stats.pearsonr(sampled_parameters[:,0], optimized_alphas_taskg[j,:])\n",
    "    \n",
    "    pearsons_correlations_betas[j] , p_val_beta = sp.stats.pearsonr(sampled_parameters[:,1], optimized_betas_taskg[j,:])\n",
    "\n",
    "print(pearsons_correlations_alphas)\n",
    "print(pearsons_correlations_betas)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "alpha-constant",
   "metadata": {},
   "source": [
    "## Task (h): Alternative model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "incomplete-killing",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Simulation Parameters\n",
    "trials = 160\n",
    "N = 10000\n",
    "\n",
    "#Simulation function of Model 1\n",
    "def model2_simulate(alpha, beta, A,V_0):  \n",
    "    \n",
    "    c = np.zeros(trials)\n",
    "    o = np.zeros(trials)\n",
    "    V_a = np.zeros(trials)\n",
    "    V_b = np.zeros(trials)\n",
    "    \n",
    "    #Initial conditions\n",
    "    V_a[0] = V_0\n",
    "    V_b[0] = V_0\n",
    "    \n",
    "    #First 40 trial set\n",
    "    for t in range(0,40):\n",
    "        \n",
    "        #Probability of choosing A\n",
    "        p_choose_A = 1/(1 + np.exp(beta*(V_a[t]-V_b[t])))\n",
    "        \n",
    "        #If A is chosen\n",
    "        if np.random.rand() < p_choose_A:\n",
    "            \n",
    "            c[t] = 1 \n",
    "            \n",
    "            #Will give aversive outcome with p = 0.6\n",
    "            if np.random.rand() < 0.6:\n",
    "                \n",
    "                o[t] = 1\n",
    "            \n",
    "            #Update V_a but not V_b\n",
    "            V_a[t+1] =  A*V_a[t] + alpha*(o[t] - V_a[t])\n",
    "            V_b[t+1] =  V_b[t] \n",
    "        \n",
    "        #If B is chosen\n",
    "        else:\n",
    "            \n",
    "            c[t] = 2\n",
    "            \n",
    "            #Will give aversive outcome with p = 0.4\n",
    "            if np.random.rand() < 0.4:\n",
    "                \n",
    "                o[t] = 1\n",
    "        \n",
    "            #Update V_b but not V_a\n",
    "            V_a[t+1] =  V_a[t] \n",
    "            V_b[t+1] =  A*V_b[t] + alpha*(o[t] - V_b[t])\n",
    "                \n",
    "    #Second 40 trial set\n",
    "    for t in range(40,80):\n",
    "        \n",
    "        #Probability of choosing A\n",
    "        p_choose_A = 1/(1 + np.exp(beta*(V_a[t]-V_b[t])))\n",
    "        \n",
    "        if np.random.rand() < p_choose_A:\n",
    "            \n",
    "            c[t] = 1\n",
    "            \n",
    "            if np.random.rand() < 0.8:\n",
    "            \n",
    "                o[t] = 1\n",
    "            \n",
    "            V_a[t+1] =  A*V_a[t] + alpha*(o[t] - V_a[t])\n",
    "            V_b[t+1] =  V_b[t] \n",
    "            \n",
    "        else:\n",
    "            \n",
    "            c[t] = 2\n",
    "            \n",
    "            if np.random.rand() < 0.2:\n",
    "                \n",
    "                o[t] = 1\n",
    "        \n",
    "            V_a[t+1] =  V_a[t] \n",
    "            V_b[t+1] =  A*V_b[t] + alpha*(o[t] - V_b[t])\n",
    "                \n",
    "    #Third 40 trial set        \n",
    "    for t in range(80,120):\n",
    "        \n",
    "        p_choose_A = 1/(1 + np.exp(beta*(V_a[t]-V_b[t])))\n",
    "        \n",
    "        if np.random.rand() < p_choose_A:\n",
    "            \n",
    "            c[t] = 1\n",
    "            \n",
    "            if np.random.rand() < 0.6:\n",
    "                \n",
    "                o[t] = 1\n",
    "            \n",
    "            V_a[t+1] =  A*V_a[t] + alpha*(o[t] - V_a[t])\n",
    "            V_b[t+1] =  V_b[t]\n",
    "            \n",
    "        else:\n",
    "            \n",
    "            c[t] = 2\n",
    "            \n",
    "            if np.random.rand() < 0.4:\n",
    "            \n",
    "                o[t] = 1\n",
    "        \n",
    "            V_a[t+1] =  V_a[t] \n",
    "            V_b[t+1] =  A*V_b[t] + alpha*(o[t] - V_b[t])       \n",
    "    \n",
    "    #Fourth 40 trial set         \n",
    "    for t in range(120,159):\n",
    "        \n",
    "        p_choose_A = 1/(1 + np.exp(beta*(V_a[t]-V_b[t])))\n",
    "        \n",
    "        if np.random.rand() < p_choose_A:\n",
    "            \n",
    "            c[t] = 1\n",
    "            \n",
    "            if np.random.rand() < 0.65:\n",
    "                \n",
    "                o[t] = 1\n",
    "            \n",
    "            V_a[t+1] =  A*V_a[t] + alpha*(o[t] - V_a[t])\n",
    "            V_b[t+1] =  V_b[t]\n",
    "            \n",
    "        else:\n",
    "            \n",
    "            c[t] = 2\n",
    "            \n",
    "            if np.random.rand() < 0.35:\n",
    "                \n",
    "                o[t] = 1\n",
    "\n",
    "            V_a[t+1] =  V_a[t] \n",
    "            V_b[t+1] =  A*V_b[t] + alpha*(o[t] - V_b[t])      \n",
    "    \n",
    "    #Last trial\n",
    "    p_choose_A = 1/(1 + np.exp(beta*(V_a[159]-V_b[159])))\n",
    "    \n",
    "    if np.random.rand() < p_choose_A:\n",
    "            \n",
    "        c[159] = 1\n",
    "            \n",
    "        if np.random.rand() < 0.65:\n",
    "                \n",
    "            o[159] = 1\n",
    "    else:\n",
    "            \n",
    "        c[159] = 2\n",
    "            \n",
    "        if np.random.rand() < 0.35:\n",
    "                \n",
    "            o[159] = 1\n",
    "    \n",
    "    return c, o, V_a, V_b\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "wooden-oasis",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  6%|▌         | 3/50 [00:01<00:16,  2.94it/s]/tmp/ipykernel_73/907251431.py:26: RuntimeWarning: overflow encountered in exp\n",
      "  choice_probabilities[t] = 1/(1 + np.exp(beta*(V[c-1]-V[c_alt-1])))\n",
      "/tmp/ipykernel_73/907251431.py:30: RuntimeWarning: divide by zero encountered in log\n",
      "  return -np.sum(np.log(choice_probabilities))\n",
      "100%|██████████| 50/50 [00:36<00:00,  1.36it/s]\n"
     ]
    }
   ],
   "source": [
    "#Fit parameter values to simulated data sets\n",
    "\n",
    "def model2_neg_log_likelihood(theta,choices,outcomes,V_0):\n",
    "    \n",
    "    alpha = theta[0]\n",
    "    beta = theta[1]\n",
    "    A = theta[2]\n",
    "    \n",
    "    V = np.array([V_0,V_0])\n",
    "\n",
    "    choice_probabilities = np.zeros(trials)\n",
    "    \n",
    "    for t in range(trials):\n",
    "        \n",
    "        c = int(choices[t])\n",
    "        o = outcomes[t]\n",
    "        \n",
    "        if c == 1:\n",
    "            \n",
    "            c_alt = 2\n",
    "        \n",
    "        else:\n",
    "            \n",
    "            c_alt = 1\n",
    "        \n",
    "        choice_probabilities[t] = 1/(1 + np.exp(beta*(V[c-1]-V[c_alt-1])))\n",
    "        \n",
    "        V[c-1] = np.copy(A*V[c-1]+ alpha*(o - V[c-1]))\n",
    "        \n",
    "    return -np.sum(np.log(choice_probabilities))\n",
    "\n",
    "optimized_alphas_mod2 = np.zeros(50)\n",
    "optimized_betas_mod2 = np.zeros(50)\n",
    "optimized_As_mod2 = np.zeros(50)\n",
    "nll_model2 = np.zeros(50) \n",
    "\n",
    "#set starting parameters\n",
    "theta_guess_mod2 = np.array([0.4,5,0.5])\n",
    "\n",
    "for i in tqdm(range(50)):\n",
    "   \n",
    "    optimized_taskh = sp.optimize.minimize(model2_neg_log_likelihood, theta_guess_mod2, args=(choices.loc[i,:], outcomes.loc[i,:] ,0.5), method='Nelder-Mead').x\n",
    "    optimized_alphas_mod2[i] = optimized_taskh[0]\n",
    "    optimized_betas_mod2[i] =  optimized_taskh[1]\n",
    "    optimized_As_mod2[i] =  optimized_taskh[2]\n",
    "    theta_nll_model2 = np.array([optimized_alphas_mod2[i],optimized_betas_mod2[i],optimized_As_mod2[i]])\n",
    "    nll_model2[i] = model2_neg_log_likelihood(theta_nll_model2,choices.loc[i,:],outcomes.loc[i,:] ,0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "catholic-reset",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson´s correlation coefficient between alpha and beta across all participants for model 2 is: -0.6112565206491124\n",
      "The Pearson´s correlation coefficient between alpha and A across all participants for model 2 is: 0.9999403636400976\n",
      "The Pearson´s correlation coefficient between beta and A across all participants for model 2 is: -0.6120314688651913\n"
     ]
    }
   ],
   "source": [
    "#Calculate Pearson´s correlation coefficient between estimated parameters across all participants for model 2\n",
    "\n",
    "pearsons_corr_alpha_beta_mod2, p_val_all = sp.stats.pearsonr(optimized_alphas_mod2, optimized_betas_mod2)\n",
    "\n",
    "print(\"The Pearson´s correlation coefficient between alpha and beta across all participants for model 2 is: \" + str(pearsons_corr_alpha_beta_mod2))\n",
    "\n",
    "pearsons_corr_alpha_A_mod2, p_val_all = sp.stats.pearsonr(optimized_alphas_mod2, optimized_As_mod2)\n",
    "\n",
    "print(\"The Pearson´s correlation coefficient between alpha and A across all participants for model 2 is: \" + str(pearsons_corr_alpha_A_mod2))\n",
    "\n",
    "pearsons_corr_beta_A_mod2, p_val_all = sp.stats.pearsonr(optimized_betas_mod2, optimized_As_mod2)\n",
    "\n",
    "print(\"The Pearson´s correlation coefficient between beta and A across all participants for model 2 is: \" + str(pearsons_corr_beta_A_mod2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "industrial-macro",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8.293316353023684\n",
      "11.11035313220925\n",
      "2.975843860244161\n",
      "3.299383541292451\n",
      "8.87831968447996\n",
      "11.128049688913112\n"
     ]
    }
   ],
   "source": [
    "print(np.mean(optimized_alphas_mod2))\n",
    "print(np.std(optimized_alphas_mod2))\n",
    "\n",
    "print(np.mean(optimized_betas_mod2))\n",
    "print(np.std(optimized_betas_mod2))\n",
    "\n",
    "print(np.mean(optimized_As_mod2))\n",
    "print(np.std(optimized_As_mod2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "hourly-majority",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Plot Model 2 fitting\n",
    "\n",
    "plt.scatter(np.linspace(1,25,25),optimized_alphas_mod2[:25], color = 'red', label = \"Anxious\")\n",
    "plt.scatter(np.linspace(26,50,25),optimized_alphas_mod2[25:], color = 'green',label = \"Control\")\n",
    "plt.title(\"Fitted learning rate \" r'$\\alpha$'\" (model 2)\",fontsize=20,**font)\n",
    "plt.xlabel(\"Participant index\",fontsize=20,**font)\n",
    "plt.ylabel(\"Parameter value\",fontsize=20,**font)\n",
    "plt.axhline(y = np.mean(optimized_alphas_mod2) + np.std(optimized_alphas_mod2),linestyle = ':')\n",
    "plt.axhline(y = np.mean(optimized_alphas_mod2),linestyle = '-')\n",
    "plt.axhline(y = np.mean(optimized_alphas_mod2) - np.std(optimized_alphas_mod2),linestyle = ':')\n",
    "plt.tick_params(axis='both', which='major', labelsize=15)\n",
    "plt.legend(fontsize=13,loc = 'upper right').get_frame().set_linewidth(1.5)\n",
    "plt.show()\n",
    "\n",
    "plt.scatter(np.linspace(1,25,25),optimized_betas_mod2[:25], color = 'red',label = \"Anxious\")\n",
    "plt.scatter(np.linspace(26,50,25),optimized_betas_mod2[25:], color = 'green',label = \"Control\")\n",
    "plt.title(\"Fitted inverse temperature \" r'$\\beta$' \" (model 2)\",fontsize=20,**font)\n",
    "plt.xlabel(\"Participant index\",fontsize=20,**font)\n",
    "plt.ylabel(\"Parameter value\",fontsize=20,**font)\n",
    "plt.axhline(y = np.mean(optimized_betas_mod2) + np.std(optimized_betas_mod2),linestyle = ':')\n",
    "plt.axhline(y = np.mean(optimized_betas_mod2),linestyle = '-')\n",
    "plt.axhline(y = np.mean(optimized_betas_mod2) - np.std(optimized_betas_mod2),linestyle = ':')\n",
    "plt.legend(fontsize=13).get_frame().set_linewidth(1.5)\n",
    "plt.tick_params(axis='both', which='major', labelsize=15)\n",
    "plt.show()\n",
    "\n",
    "plt.scatter(np.linspace(1,25,25),optimized_As_mod2[:25], color = 'red',label = \"Anxious\")\n",
    "plt.scatter(np.linspace(26,50,25),optimized_As_mod2[25:], color = 'green',label = \"Control\")\n",
    "plt.title(\"Fitted A parameter (model 2)\",fontsize=20,**font)\n",
    "plt.xlabel(\"Participant index\",fontsize=20,**font)\n",
    "plt.ylabel(\"Parameter value\",fontsize=20,**font)\n",
    "plt.axhline(y = np.mean(optimized_As_mod2) + np.std(optimized_As_mod2),linestyle = ':')\n",
    "plt.axhline(y = np.mean(optimized_As_mod2),linestyle = '-')\n",
    "plt.axhline(y = np.mean(optimized_As_mod2) - np.std(optimized_As_mod2),linestyle = ':')\n",
    "plt.legend(fontsize=13).get_frame().set_linewidth(1.5)\n",
    "plt.tick_params(axis='both', which='major', labelsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "clear-promotion",
   "metadata": {},
   "source": [
    "## Task (k): Discussion and extra model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "handed-shell",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Simulation Parameters\n",
    "\n",
    "N = 10000\n",
    "\n",
    "#Simulation function of Model 3\n",
    "def model3_simulate(theta_mod3,V_0):  \n",
    "    \n",
    "    alpha_p = theta_mod3[0]\n",
    "    alpha_m = theta_mod3[1]\n",
    "    beta = theta_mod3[2]\n",
    "    \n",
    "    \n",
    "    c = np.zeros(trials)\n",
    "    o = np.zeros(trials)\n",
    "    V_a = np.zeros(trials)\n",
    "    V_b = np.zeros(trials)\n",
    "    \n",
    "    #Initial conditions\n",
    "    V_a[0] = V_0\n",
    "    V_b[0] = V_0\n",
    "    \n",
    "    #First 40 trial set\n",
    "    for t in range(0,40):\n",
    "        \n",
    "        #Probability of choosing A\n",
    "        p_choose_A = 1/(1 + np.exp(beta*(V_a[t]-V_b[t])))\n",
    "        \n",
    "        #If A is chosen\n",
    "        if np.random.rand() < p_choose_A:\n",
    "            \n",
    "            c[t] = 1 \n",
    "            \n",
    "            #Will give aversive outcome with p = 0.6\n",
    "            if np.random.rand() < 0.6:\n",
    "                \n",
    "                o[t] = 1\n",
    "            \n",
    "            #Update V_a but not V_b\n",
    "            V_a[t+1] =  V_a[t] + ((1-o[t])*alpha_p +o[t]*alpha_m)*(o[t] - V_a[t])\n",
    "            V_b[t+1] =  V_b[t] \n",
    "        \n",
    "        #If B is chosen\n",
    "        else:\n",
    "            \n",
    "            c[t] = 2\n",
    "            \n",
    "            #Will give aversive outcome with p = 0.4\n",
    "            if np.random.rand() < 0.4:\n",
    "                \n",
    "                o[t] = 1\n",
    "        \n",
    "            #Update V_b but not V_a\n",
    "            V_a[t+1] =  V_a[t] \n",
    "            V_b[t+1] =  V_b[t] + ((1-o[t])*alpha_p +o[t]*alpha_m)*(o[t] - V_b[t])\n",
    "                \n",
    "    #Second 40 trial set\n",
    "    for t in range(40,80):\n",
    "        \n",
    "        #Probability of choosing A\n",
    "        p_choose_A = 1/(1 + np.exp(beta*(V_a[t]-V_b[t])))\n",
    "        \n",
    "        if np.random.rand() < p_choose_A:\n",
    "            \n",
    "            c[t] = 1\n",
    "            \n",
    "            if np.random.rand() < 0.8:\n",
    "            \n",
    "                o[t] = 1\n",
    "            \n",
    "            V_a[t+1] =  V_a[t] + ((1-o[t])*alpha_p +o[t]*alpha_m)*(o[t] - V_a[t])\n",
    "            V_b[t+1] =  V_b[t] \n",
    "            \n",
    "        else:\n",
    "            \n",
    "            c[t] = 2\n",
    "            \n",
    "            if np.random.rand() < 0.2:\n",
    "                \n",
    "                o[t] = 1\n",
    "        \n",
    "            V_a[t+1] =  V_a[t] \n",
    "            V_b[t+1] =  V_b[t] + ((1-o[t])*alpha_p + o[t]*alpha_m)*(o[t] - V_b[t])\n",
    "                \n",
    "    #Third 40 trial set        \n",
    "    for t in range(80,120):\n",
    "        \n",
    "        p_choose_A = 1/(1 + np.exp(beta*(V_a[t]-V_b[t])))\n",
    "        \n",
    "        if np.random.rand() < p_choose_A:\n",
    "            \n",
    "            c[t] = 1\n",
    "            \n",
    "            if np.random.rand() < 0.6:\n",
    "                \n",
    "                o[t] = 1\n",
    "            \n",
    "            V_a[t+1] =  V_a[t] + ((1-o[t])*alpha_p + o[t]*alpha_m)*(o[t] - V_a[t])\n",
    "            V_b[t+1] =  V_b[t]\n",
    "            \n",
    "        else:\n",
    "            \n",
    "            c[t] = 2\n",
    "            \n",
    "            if np.random.rand() < 0.4:\n",
    "            \n",
    "                o[t] = 1\n",
    "        \n",
    "            V_a[t+1] =  V_a[t] \n",
    "            V_b[t+1] =  V_b[t] + ((1-o[t])*alpha_p + o[t]*alpha_m)*(o[t] - V_b[t])  \n",
    "    \n",
    "    #Fourth 40 trial set         \n",
    "    for t in range(120,159):\n",
    "        \n",
    "        p_choose_A = 1/(1 + np.exp(beta*(V_a[t]-V_b[t])))\n",
    "        \n",
    "        if np.random.rand() < p_choose_A:\n",
    "            \n",
    "            c[t] = 1\n",
    "            \n",
    "            if np.random.rand() < 0.65:\n",
    "                \n",
    "                o[t] = 1\n",
    "            \n",
    "            V_a[t+1] =  V_a[t] + ((1-o[t])*alpha_p + o[t]*alpha_m)*(o[t] - V_a[t]) \n",
    "            V_b[t+1] =  V_b[t]\n",
    "            \n",
    "        else:\n",
    "            \n",
    "            c[t] = 2\n",
    "            \n",
    "            if np.random.rand() < 0.35:\n",
    "                \n",
    "                o[t] = 1\n",
    "\n",
    "            V_a[t+1] =  V_a[t] \n",
    "            V_b[t+1] =  V_b[t] + ((1-o[t])*alpha_p + o[t]*alpha_m)*(o[t] - V_b[t])\n",
    "    \n",
    "    #Last trial\n",
    "    p_choose_A = 1/(1 + np.exp(beta*(V_a[159]-V_b[159])))\n",
    "    \n",
    "    if np.random.rand() < p_choose_A:\n",
    "            \n",
    "        c[159] = 1\n",
    "            \n",
    "        if np.random.rand() < 0.65:\n",
    "                \n",
    "            o[159] = 1\n",
    "    else:\n",
    "            \n",
    "        c[159] = 2\n",
    "            \n",
    "        if np.random.rand() < 0.35:\n",
    "                \n",
    "            o[159] = 1\n",
    "    \n",
    "    return c, o, V_a, V_b\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "marine-anger",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 50/50 [00:20<00:00,  2.40it/s]\n"
     ]
    }
   ],
   "source": [
    "#Fit parameter values to simulated data sets for model 3\n",
    "\n",
    "def model3_neg_log_likelihood(theta_mod3,choices,outcomes,V_0):\n",
    "    \n",
    "    alpha_p = theta_mod3[0]\n",
    "    alpha_m = theta_mod3[1]\n",
    "    beta = theta_mod3[2]\n",
    "    \n",
    "    V = np.array([V_0,V_0])\n",
    "\n",
    "    choice_probabilities = np.zeros(trials)\n",
    "    \n",
    "    for t in range(trials):\n",
    "        \n",
    "        c = int(choices[t])\n",
    "        o = outcomes[t]\n",
    "        \n",
    "        if c == 1:\n",
    "            \n",
    "            c_alt = 2\n",
    "        \n",
    "        else:\n",
    "            \n",
    "            c_alt = 1\n",
    "        \n",
    "        choice_probabilities[t] = 1/(1 + np.exp(beta*(V[c-1]-V[c_alt-1])))\n",
    "        \n",
    "        V[c-1] = np.copy(V[c-1]+ ((1-o)*alpha_p + o*alpha_m)*(o - V[c-1]))\n",
    "        \n",
    "    return -np.sum(np.log(choice_probabilities))\n",
    "\n",
    "optimized_alphas_p_mod3 = np.zeros(50)\n",
    "optimized_alphas_m_mod3 = np.zeros(50)\n",
    "optimized_betas_mod3 = np.zeros(50)\n",
    "\n",
    "nll_model3 = np.zeros(50) \n",
    "\n",
    "#set starting parameters\n",
    "theta_guess_mod3 = np.array([0.25,0.35,6])\n",
    "\n",
    "for i in tqdm(range(50)):\n",
    "    optimizied_task_k = sp.optimize.minimize(model3_neg_log_likelihood, theta_guess_mod3, args=(choices.loc[i,:], outcomes.loc[i,:] ,0.5), method='Nelder-Mead').x\n",
    "    optimized_alphas_p_mod3[i] = optimizied_task_k[0]\n",
    "    optimized_alphas_m_mod3[i] = optimizied_task_k[1]\n",
    "    optimized_betas_mod3[i] =  optimizied_task_k[2]\n",
    "    theta_nll_model3 = np.array([optimized_alphas_p_mod3[i],optimized_alphas_m_mod3[i],optimized_betas_mod3[i]])\n",
    "    nll_model3[i] = model3_neg_log_likelihood(theta_nll_model3,choices.loc[i,:],outcomes.loc[i,:] ,0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "attended-intake",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson´s correlation coefficient between alpha plus and alpha minus across all participants for model 3 is: 0.03321450980822904\n",
      "The Pearson´s correlation coefficient between alpha plus and beta across all participants for model 3 is: -0.44054161906594685\n",
      "The Pearson´s correlation coefficient between alpha m and beta across all participants for model 3 is: 0.3710066996746164\n"
     ]
    }
   ],
   "source": [
    "#Calculate Pearson´s correlation coefficient between estimated parameters across all participants for model 2\n",
    "\n",
    "pearsons_corr_alpha_p_alpha_m_mod3, p_val_all = sp.stats.pearsonr(optimized_alphas_p_mod3, optimized_alphas_m_mod3)\n",
    "\n",
    "print(\"The Pearson´s correlation coefficient between alpha plus and alpha minus across all participants for model 3 is: \" + str(pearsons_corr_alpha_p_alpha_m_mod3))\n",
    "\n",
    "pearsons_corr_alpha_p_betas_mod3, p_val_all = sp.stats.pearsonr(optimized_alphas_p_mod3, optimized_betas_mod3)\n",
    "\n",
    "print(\"The Pearson´s correlation coefficient between alpha plus and beta across all participants for model 3 is: \" + str(pearsons_corr_alpha_p_betas_mod3))\n",
    "\n",
    "pearsons_corr_alpha_m_betas_mod3, p_val_all = sp.stats.pearsonr(optimized_alphas_m_mod3, optimized_betas_mod3)\n",
    "\n",
    "print(\"The Pearson´s correlation coefficient between alpha m and beta across all participants for model 3 is: \" + str(pearsons_corr_alpha_m_betas_mod3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "incident-chase",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ttest_indResult(statistic=0.9787552608936594, pvalue=0.332609865908139)\n",
      "Ttest_indResult(statistic=2.836906778297149, pvalue=0.006653256862702414)\n",
      "Ttest_indResult(statistic=1.7226035623246954, pvalue=0.09621603471084636)\n"
     ]
    }
   ],
   "source": [
    "# Welsch t-test\n",
    "print(stats.ttest_ind(optimized_alphas_p_mod3[:25],optimized_alphas_p_mod3[25:] , equal_var=False))\n",
    "print(stats.ttest_ind(optimized_alphas_m_mod3[:25],optimized_alphas_m_mod3[25:] , equal_var=False))\n",
    "print(stats.ttest_ind(optimized_betas_mod3[:25],optimized_betas_mod3[25:] , equal_var=False))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "banned-stopping",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Plot Model 3 fitting\n",
    "\n",
    "plt.scatter(np.linspace(1,25,25),optimized_alphas_p_mod3[:25], color = 'red', label = \"Anxious\")\n",
    "plt.scatter(np.linspace(26,50,25),optimized_alphas_p_mod3[25:], color = 'green',label = \"Control\")\n",
    "plt.title(\"Fitted neutral outcome learning rate \" r'$\\alpha^{+}$'\" (model 3)\",fontsize=20,**font)\n",
    "plt.xlabel(\"Participant index\",fontsize=20,**font)\n",
    "plt.ylabel(\"Parameter value\",fontsize=20,**font)\n",
    "plt.axhline(y = np.mean(optimized_alphas_p_mod3) + np.std(optimized_alphas_p_mod3),linestyle = ':')\n",
    "plt.axhline(y = np.mean(optimized_alphas_p_mod3),linestyle = '-')\n",
    "plt.axhline(y = np.mean(optimized_alphas_p_mod3) - np.std(optimized_alphas_p_mod3),linestyle = ':')\n",
    "plt.tick_params(axis='both', which='major', labelsize=15)\n",
    "plt.legend(fontsize=13,loc = 'upper right').get_frame().set_linewidth(1.5)\n",
    "plt.show()\n",
    "\n",
    "plt.scatter(np.linspace(1,25,25),optimized_alphas_m_mod3[:25], color = 'red', label = \"Anxious\")\n",
    "plt.scatter(np.linspace(26,50,25),optimized_alphas_m_mod3[25:], color = 'green',label = \"Control\")\n",
    "plt.title(\"Fitted punishment learning rate \" r'$\\alpha^{-}$'\" (model 3)\",fontsize=20,**font)\n",
    "plt.xlabel(\"Participant index\",fontsize=20,**font)\n",
    "plt.ylabel(\"Parameter value\",fontsize=20,**font)\n",
    "plt.axhline(y = np.mean(optimized_alphas_m_mod3) + np.std(optimized_alphas_m_mod3),linestyle = ':')\n",
    "plt.axhline(y = np.mean(optimized_alphas_m_mod3),linestyle = '-')\n",
    "plt.axhline(y = np.mean(optimized_alphas_m_mod3) - np.std(optimized_alphas_m_mod3),linestyle = ':')\n",
    "plt.tick_params(axis='both', which='major', labelsize=15)\n",
    "plt.legend(fontsize=13,loc = 'upper right').get_frame().set_linewidth(1.5)\n",
    "plt.show()\n",
    "\n",
    "plt.scatter(np.linspace(1,25,25),optimized_betas_mod3[:25], color = 'red',label = \"Anxious\")\n",
    "plt.scatter(np.linspace(26,50,25),optimized_betas_mod3[25:], color = 'green',label = \"Control\")\n",
    "plt.title(\"Fitted inverse temperature \" r'$\\beta$' \" (model 3)\",fontsize=20,**font)\n",
    "plt.xlabel(\"Participant index\",fontsize=20,**font)\n",
    "plt.ylabel(\"Parameter value\",fontsize=20,**font)\n",
    "plt.axhline(y = np.mean(optimized_betas_mod3) + np.std(optimized_betas_mod3),linestyle = ':')\n",
    "plt.axhline(y = np.mean(optimized_betas_mod3),linestyle = '-')\n",
    "plt.axhline(y = np.mean(optimized_betas_mod3) - np.std(optimized_betas_mod3),linestyle = ':')\n",
    "plt.legend(fontsize=13).get_frame().set_linewidth(1.5)\n",
    "plt.tick_params(axis='both', which='major', labelsize=15)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "opening-satin",
   "metadata": {},
   "source": [
    "## Task (i): Model comparison"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "seventh-level",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1224x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Plot the NLL for each particiapant for the three models:\n",
    "\n",
    "width = 0.3\n",
    "fig, ax = plt.subplots(figsize = (17,6))\n",
    "ax.bar(np.linspace(1,50,50)- width, nll_model1, width, label='Model 1')\n",
    "ax.bar(np.linspace(1,50,50), nll_model2, width, label='Model 2')\n",
    "ax.bar(np.linspace(1,50,50) + width, nll_model3, width, label='Model 3')\n",
    "plt.title(\"Negative Log-likelihood of each participant for each model\",fontsize=20,**font)\n",
    "plt.xlabel(\"Participant index\",fontsize=20,**font)\n",
    "plt.ylabel(\"Negative Log-Likelihood\",fontsize=20,**font)\n",
    "plt.legend(fontsize=15).get_frame().set_linewidth(1.5)\n",
    "plt.tick_params(axis='both', which='major', labelsize=20)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "structured-grade",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The AIC score for model 1 is: 6070.434717769935\n",
      "The AIC score for model 2 is: 6123.361893245397\n",
      "The AIC score for model 3 is: 6043.090488753161\n",
      "The BIC score for model 1 is: 6377.952099293318\n",
      "The BIC score for model 2 is: 6584.637965530471\n",
      "The BIC score for model 3 is: 6504.366561038234\n"
     ]
    }
   ],
   "source": [
    "#Compute AIC and BIC scores for each model\n",
    "\n",
    "AIC_mod1_part = np.zeros(50)\n",
    "AIC_mod2_part = np.zeros(50)\n",
    "AIC_mod3_part = np.zeros(50)\n",
    "\n",
    "BIC_mod1_part = np.zeros(50)\n",
    "BIC_mod2_part = np.zeros(50)\n",
    "BIC_mod3_part = np.zeros(50)\n",
    "\n",
    "\n",
    "\n",
    "for i in range(50):\n",
    "    \n",
    "    AIC_mod1_part[i] = 2*nll_model1[i] + 4 \n",
    "    \n",
    "    AIC_mod2_part[i] = 2*nll_model2[i] + 6\n",
    "    \n",
    "    AIC_mod3_part[i] = 2*nll_model3[i] + 6\n",
    "\n",
    "    BIC_mod1_part[i] = 2*nll_model1[i] + 2*np.log(160) \n",
    "    \n",
    "    BIC_mod2_part[i] = 2*nll_model2[i] + 3*np.log(160)\n",
    "    \n",
    "    BIC_mod3_part[i] = 2*nll_model3[i] + 3*np.log(160)\n",
    "\n",
    "print(\"The AIC score for model 1 is: \" + str(np.sum(AIC_mod1_part)))\n",
    "\n",
    "print(\"The AIC score for model 2 is: \" +str(np.sum(AIC_mod2_part)))\n",
    "\n",
    "print(\"The AIC score for model 3 is: \" +str(np.sum(AIC_mod3_part)))\n",
    "\n",
    "print(\"The BIC score for model 1 is: \" + str(np.sum(BIC_mod1_part)))\n",
    "\n",
    "print(\"The BIC score for model 2 is: \" +str(np.sum(BIC_mod2_part)))\n",
    "\n",
    "print(\"The BIC score for model 3 is: \" +str(np.sum(BIC_mod3_part)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "copyrighted-whale",
   "metadata": {},
   "source": [
    "## Task (j): Model recovery and confusion matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "geological-carpet",
   "metadata": {},
   "outputs": [],
   "source": [
    "def model1_neg_log_likelihood(theta,choices,outcomes,V_0):\n",
    "    \n",
    "    alpha = theta[0]\n",
    "    beta = theta[1]\n",
    "    \n",
    "    V = np.array([V_0,V_0])\n",
    "\n",
    "    choice_probabilities = np.zeros(trials)\n",
    "    \n",
    "    for t in range(trials):\n",
    "        \n",
    "        c = int(choices[t])\n",
    "        o = outcomes[t]\n",
    "        \n",
    "        if c == 1:\n",
    "            \n",
    "            c_alt = 2\n",
    "        \n",
    "        else:\n",
    "            \n",
    "            c_alt = 1\n",
    "        \n",
    "        choice_probabilities[t] = 1/(1 + np.exp(beta*(V[c-1]-V[c_alt-1])))\n",
    "        \n",
    "        V[c-1] = np.copy(V[c-1]+ alpha*(o - V[c-1]))\n",
    "        \n",
    "    return -np.sum(np.log(choice_probabilities))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "boring-imaging",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Covariance matrix for each model\n",
    "cov_mod1 = np.array([[0.01,0],[0,0.5]])\n",
    "cov_mod2 = np.array([[0.01,0,0],[0,0.5,0],[0,0,0.01]])\n",
    "cov_mod3 = np.array([[0.01,0,0],[0,0.01,0],[0,0,0.5]])\n",
    "\n",
    "#Initial guess for each model (optimization)\n",
    "theta_guess_mod1 = np.array([0.3,8])\n",
    "theta_guess_mod2 = np.array([0.4,5,0.5])\n",
    "theta_guess_mod3 = np.array([0.25,0.35,6])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "ignored-yesterday",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " 15%|█▌        | 15/100 [00:05<00:28,  2.99it/s]/tmp/ipykernel_73/907251431.py:26: RuntimeWarning: overflow encountered in exp\n",
      "  choice_probabilities[t] = 1/(1 + np.exp(beta*(V[c-1]-V[c_alt-1])))\n",
      "/tmp/ipykernel_73/907251431.py:30: RuntimeWarning: divide by zero encountered in log\n",
      "  return -np.sum(np.log(choice_probabilities))\n",
      "100%|██████████| 100/100 [00:39<00:00,  2.56it/s]\n"
     ]
    }
   ],
   "source": [
    "#Sample parameters model 1\n",
    "sampled_parameters_mod1 = np.random.multivariate_normal(mean_fitted,cov_mod1,100)\n",
    "\n",
    "#resample outliers in model 1\n",
    "for i in range (len(sampled_parameters_mod1[:,0])):\n",
    "    if sampled_parameters_mod1[i,0] > (0.4237 + np.sqrt(0.0143)) or sampled_parameters_mod1[i,0] < (0.4237 - np.sqrt(0.0143)):\n",
    "        new_samp = np.random.multivariate_normal(mean_fitted,cov_mod1)[0]\n",
    "        while new_samp >  (0.4237 + np.sqrt(0.0143)) or new_samp < (0.4237 - np.sqrt(0.0143)):\n",
    "            new_samp = np.random.multivariate_normal(mean_fitted,cov_mod1)[0]\n",
    "        sampled_parameters_mod1[i,0] = new_samp\n",
    "\n",
    "for i in range (len(sampled_parameters_mod1[:,1])):\n",
    "    if sampled_parameters_mod1[i,1] > (5.2790 + np.sqrt(3.0382)) or sampled_parameters_mod1[i,1] < (5.2790 - np.sqrt(3.0382)):\n",
    "\n",
    "        new_samp = np.random.multivariate_normal(mean_fitted,cov_mod1)[1]\n",
    "        while new_samp >  (5.2790 + np.sqrt(3.0382)) or new_samp < (5.2790 - np.sqrt(3.0382)):\n",
    "            new_samp = np.random.multivariate_normal(mean_fitted,cov_mod1)[1]\n",
    "        sampled_parameters_mod1[i,1] = new_samp\n",
    "\n",
    "AIC_winner_datamod1 = np.zeros(100)\n",
    "BIC_winner_datamod1 = np.zeros(100)\n",
    "        \n",
    "for i in tqdm(range(100)):\n",
    "    simulated_cho_mod1 , simulated_out_mod1 , simulated_V_a_mod1 , simulated_V_b_mod1 = model_simulate(sampled_parameters_mod1[i,0], sampled_parameters_mod1[i,1], 0.5)\n",
    "    \n",
    "    #fit models to simulated data\n",
    "    optimized_datamod1_mod1 = sp.optimize.minimize(model1_neg_log_likelihood, theta_guess_mod1, args=(simulated_cho_mod1, simulated_out_mod1 ,0.5), method='Nelder-Mead').x\n",
    "    optimized_datamod1_mod2 = sp.optimize.minimize(model2_neg_log_likelihood, theta_guess_mod2, args=(simulated_cho_mod1, simulated_out_mod1 ,0.5), method='Nelder-Mead').x\n",
    "    optimized_datamod1_mod3 = sp.optimize.minimize(model3_neg_log_likelihood, theta_guess_mod3, args=(simulated_cho_mod1, simulated_out_mod1 ,0.5), method='Nelder-Mead').x\n",
    "    \n",
    "    #compute AIC and BIC scores for model 1\n",
    "    theta_nll_datamod1_mod1 = np.array([optimized_datamod1_mod1[0],optimized_datamod1_mod1[1]])\n",
    "    nll_datamod1_mod1 = model1_neg_log_likelihood(theta_nll_datamod1_mod1,simulated_cho_mod1,simulated_out_mod1 ,0.5)\n",
    "    AIC_datamod1_mod1 = 2*nll_datamod1_mod1 + 4 \n",
    "    BIC_datamod1_mod1 = 2*nll_datamod1_mod1 + 2*np.log(160)\n",
    "    \n",
    "    #compute AIC and BIC scores for model 2\n",
    "    theta_nll_datamod1_mod2 = np.array([optimized_datamod1_mod2[0],optimized_datamod1_mod2[1],optimized_datamod1_mod2[2]])\n",
    "    nll_datamod1_mod2 = model2_neg_log_likelihood(theta_nll_datamod1_mod2,simulated_cho_mod1,simulated_out_mod1 ,0.5)\n",
    "    AIC_datamod1_mod2 = 2*nll_datamod1_mod2 + 6 \n",
    "    BIC_datamod1_mod2 = 2*nll_datamod1_mod2 + 3*np.log(160)\n",
    "    \n",
    "    #compute AIC and BIC scores for model 3\n",
    "    theta_nll_datamod1_mod3 = np.array([optimized_datamod1_mod3[0],optimized_datamod1_mod3[1],optimized_datamod1_mod3[2]])\n",
    "    nll_datamod1_mod3 = model3_neg_log_likelihood(theta_nll_datamod1_mod3,simulated_cho_mod1,simulated_out_mod1 ,0.5)\n",
    "    AIC_datamod1_mod3 = 2*nll_datamod1_mod3 + 6 \n",
    "    BIC_datamod1_mod3 = 2*nll_datamod1_mod3 + 3*np.log(160)\n",
    "    \n",
    "    #Compare AICS:\n",
    "    AICs_datamod1 = np.array([AIC_datamod1_mod1,AIC_datamod1_mod2,AIC_datamod1_mod3])\n",
    "    AIC_winner_datamod1[i] =np.argmin(AICs_datamod1)\n",
    "    \n",
    "    #Compare BICS:\n",
    "    BICs_datamod1 = np.array([BIC_datamod1_mod1,BIC_datamod1_mod2,BIC_datamod1_mod3])\n",
    "    BIC_winner_datamod1[i] =np.argmin(BICs_datamod1)\n",
    "    \n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "forty-spanking",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  0%|          | 0/100 [00:00<?, ?it/s]/tmp/ipykernel_73/907251431.py:26: RuntimeWarning: overflow encountered in exp\n",
      "  choice_probabilities[t] = 1/(1 + np.exp(beta*(V[c-1]-V[c_alt-1])))\n",
      "/tmp/ipykernel_73/907251431.py:30: RuntimeWarning: divide by zero encountered in log\n",
      "  return -np.sum(np.log(choice_probabilities))\n",
      " 24%|██▍       | 24/100 [00:15<00:47,  1.60it/s]/tmp/ipykernel_73/15715216.py:23: RuntimeWarning: overflow encountered in exp\n",
      "  choice_probabilities[t] = 1/(1 + np.exp(beta*(V[c-1]-V[c_alt-1])))\n",
      "/tmp/ipykernel_73/15715216.py:27: RuntimeWarning: divide by zero encountered in log\n",
      "  return -np.sum(np.log(choice_probabilities))\n",
      "100%|██████████| 100/100 [01:04<00:00,  1.56it/s]\n"
     ]
    }
   ],
   "source": [
    "mean_fitted_mod2 = np.array([np.mean(optimized_alphas_mod2),np.mean(optimized_betas_mod2),np.mean(optimized_As_mod2)])\n",
    "std_fitted_mod2 = np.array([np.std(optimized_alphas_mod2),np.std(optimized_betas_mod2),np.std(optimized_As_mod2)])\n",
    "\n",
    "\n",
    "#Sample parameters model 2\n",
    "sampled_parameters_mod2 = np.random.multivariate_normal(mean_fitted_mod2,cov_mod2,100)\n",
    "\n",
    "#resample outliers in model 2\n",
    "for i in range (len(sampled_parameters_mod2[:,0])):\n",
    "    if sampled_parameters_mod2[i,0] > (mean_fitted_mod2[0] + std_fitted_mod2[0])  or sampled_parameters_mod2[i,0] < (mean_fitted_mod2[0] - std_fitted_mod2[0]):\n",
    "        new_samp = np.random.multivariate_normal(mean_fitted_mod2,cov_mod2)[0]\n",
    "        while new_samp >  (mean_fitted_mod2[0] + std_fitted_mod2[0]) or new_samp < (mean_fitted_mod2[0] - std_fitted_mod2[0]):\n",
    "            new_samp = np.random.multivariate_normal(mean_fitted_mod2,cov_mod2)[0]\n",
    "        sampled_parameters_mod2[i,0] = new_samp\n",
    "        \n",
    "for i in range (len(sampled_parameters_mod2[:,1])):\n",
    "    if sampled_parameters_mod2[i,1] > (mean_fitted_mod2[1] + std_fitted_mod2[1])  or sampled_parameters_mod2[i,1] < (mean_fitted_mod2[1] - std_fitted_mod2[1]):\n",
    "        new_samp = np.random.multivariate_normal(mean_fitted_mod2,cov_mod2)[1]\n",
    "        while new_samp >  (mean_fitted_mod2[1] + std_fitted_mod2[1]) or new_samp < (mean_fitted_mod2[1] - std_fitted_mod2[1]):\n",
    "            new_samp = np.random.multivariate_normal(mean_fitted_mod2,cov_mod2)[1]\n",
    "        sampled_parameters_mod2[i,1] = new_samp\n",
    "\n",
    "for i in range (len(sampled_parameters_mod2[:,2])):\n",
    "    if sampled_parameters_mod2[i,2] > (mean_fitted_mod2[2] + std_fitted_mod2[2])  or sampled_parameters_mod2[i,2] < (mean_fitted_mod2[2] - std_fitted_mod2[2]):\n",
    "        new_samp = np.random.multivariate_normal(mean_fitted_mod2,cov_mod2)[2]\n",
    "        while new_samp >  (mean_fitted_mod2[2] + std_fitted_mod2[2]) or new_samp < (mean_fitted_mod2[2] - std_fitted_mod2[2]):\n",
    "            new_samp = np.random.multivariate_normal(mean_fitted_mod2,cov_mod2)[2]\n",
    "        sampled_parameters_mod2[i,2] = new_samp\n",
    "\n",
    "AIC_winner_datamod2 = np.zeros(100)\n",
    "BIC_winner_datamod2 = np.zeros(100)\n",
    "        \n",
    "for i in tqdm(range(100)):\n",
    "    simulated_cho_mod2 , simulated_out_mod2 , simulated_V_a_mod2 , simulated_V_b_mod2 = model2_simulate(sampled_parameters_mod2[i,0], sampled_parameters_mod2[i,1], sampled_parameters_mod2[i,2],0.5)\n",
    "    \n",
    "    #fit models to simulated data\n",
    "    optimized_datamod2_mod1 = sp.optimize.minimize(model1_neg_log_likelihood, theta_guess_mod1, args=(simulated_cho_mod2, simulated_out_mod2 ,0.5), method='Nelder-Mead').x\n",
    "    optimized_datamod2_mod2 = sp.optimize.minimize(model2_neg_log_likelihood, theta_guess_mod2, args=(simulated_cho_mod2, simulated_out_mod2 ,0.5), method='Nelder-Mead').x\n",
    "    optimized_datamod2_mod3 = sp.optimize.minimize(model3_neg_log_likelihood, theta_guess_mod3, args=(simulated_cho_mod2, simulated_out_mod2 ,0.5), method='Nelder-Mead').x\n",
    "    \n",
    "    #compute AIC and BIC scores for model 1\n",
    "    theta_nll_datamod2_mod1 = np.array([optimized_datamod2_mod1[0],optimized_datamod2_mod1[1]])\n",
    "    nll_datamod2_mod1 = model1_neg_log_likelihood(theta_nll_datamod2_mod1,simulated_cho_mod2,simulated_out_mod2 ,0.5)\n",
    "    AIC_datamod2_mod1 = 2*nll_datamod2_mod1 + 4 \n",
    "    BIC_datamod2_mod1 = 2*nll_datamod2_mod1 + 2*np.log(160)\n",
    "    \n",
    "    #compute AIC and BIC scores for model 2\n",
    "    theta_nll_datamod2_mod2 = np.array([optimized_datamod2_mod2[0],optimized_datamod2_mod2[1],optimized_datamod2_mod2[2]])\n",
    "    nll_datamod2_mod2 = model2_neg_log_likelihood(theta_nll_datamod1_mod2,simulated_cho_mod2,simulated_out_mod2 ,0.5)\n",
    "    AIC_datamod2_mod2 = 2*nll_datamod2_mod2 + 6 \n",
    "    BIC_datamod2_mod2 = 2*nll_datamod2_mod2 + 3*np.log(160)\n",
    "    \n",
    "    #compute AIC and BIC scores for model 3\n",
    "    theta_nll_datamod2_mod3 = np.array([optimized_datamod2_mod3[0],optimized_datamod2_mod3[1],optimized_datamod2_mod3[2]])\n",
    "    nll_datamod2_mod3 = model3_neg_log_likelihood(theta_nll_datamod2_mod3,simulated_cho_mod2,simulated_out_mod2 ,0.5)\n",
    "    AIC_datamod2_mod3 = 2*nll_datamod2_mod3 + 6 \n",
    "    BIC_datamod2_mod3 = 2*nll_datamod2_mod3 + 3*np.log(160)\n",
    "    \n",
    "    #Compare AICS:\n",
    "    AICs_datamod2 = np.array([AIC_datamod2_mod1,AIC_datamod2_mod2,AIC_datamod2_mod3])\n",
    "    AIC_winner_datamod2[i] = np.argmin(AICs_datamod2)\n",
    "    \n",
    "    #Compare BICS:\n",
    "    BICs_datamod2 = np.array([BIC_datamod2_mod1,BIC_datamod2_mod2,BIC_datamod2_mod3])\n",
    "    BIC_winner_datamod2[i] =np.argmin(BICs_datamod2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "specific-schema",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  5%|▌         | 5/100 [00:01<00:31,  3.03it/s]/tmp/ipykernel_73/907251431.py:26: RuntimeWarning: overflow encountered in exp\n",
      "  choice_probabilities[t] = 1/(1 + np.exp(beta*(V[c-1]-V[c_alt-1])))\n",
      "/tmp/ipykernel_73/907251431.py:30: RuntimeWarning: divide by zero encountered in log\n",
      "  return -np.sum(np.log(choice_probabilities))\n",
      "100%|██████████| 100/100 [00:41<00:00,  2.41it/s]\n"
     ]
    }
   ],
   "source": [
    "mean_fitted_mod3 = np.array([np.mean(optimized_alphas_p_mod3),np.mean(optimized_alphas_m_mod3),np.mean(optimized_betas_mod3)])\n",
    "std_fitted_mod3 = np.array([np.std(optimized_alphas_p_mod3),np.std(optimized_alphas_m_mod3),np.std(optimized_betas_mod3)])\n",
    "\n",
    "#Sample parameters model 3\n",
    "sampled_parameters_mod3 = np.random.multivariate_normal(mean_fitted_mod3,cov_mod3,100)\n",
    "\n",
    "#resample outliers in model 3\n",
    "for i in range (len(sampled_parameters_mod3[:,0])):\n",
    "    if sampled_parameters_mod3[i,0] > (mean_fitted_mod3[0] + std_fitted_mod3[0])  or sampled_parameters_mod3[i,0] < (mean_fitted_mod3[0] - std_fitted_mod3[0]):\n",
    "        new_samp = np.random.multivariate_normal(mean_fitted_mod3,cov_mod3)[0]\n",
    "        while new_samp >  (mean_fitted_mod3[0] + std_fitted_mod3[0]) or new_samp < (mean_fitted_mod3[0] - std_fitted_mod3[0]):\n",
    "            new_samp = np.random.multivariate_normal(mean_fitted_mod3,cov_mod3)[0]\n",
    "        sampled_parameters_mod3[i,0] = new_samp\n",
    "        \n",
    "for i in range (len(sampled_parameters_mod3[:,1])):\n",
    "    if sampled_parameters_mod3[i,1] > (mean_fitted_mod3[1] + std_fitted_mod3[1])  or sampled_parameters_mod3[i,1] < (mean_fitted_mod3[1] - std_fitted_mod3[1]):\n",
    "        new_samp = np.random.multivariate_normal(mean_fitted_mod3,cov_mod3)[1]\n",
    "        while new_samp >  (mean_fitted_mod3[1] + std_fitted_mod3[1]) or new_samp < (mean_fitted_mod3[1] - std_fitted_mod3[1]):\n",
    "            new_samp = np.random.multivariate_normal(mean_fitted_mod3,cov_mod3)[1]\n",
    "        sampled_parameters_mod3[i,1] = new_samp\n",
    "\n",
    "for i in range (len(sampled_parameters_mod3[:,2])):\n",
    "    if sampled_parameters_mod3[i,2] > (mean_fitted_mod3[2] + std_fitted_mod3[2])  or sampled_parameters_mod3[i,2] < (mean_fitted_mod3[2] - std_fitted_mod3[2]):\n",
    "        new_samp = np.random.multivariate_normal(mean_fitted_mod3,cov_mod3)[2]\n",
    "        while new_samp >  (mean_fitted_mod3[2] + std_fitted_mod3[2]) or new_samp < (mean_fitted_mod3[2] - std_fitted_mod3[2]):\n",
    "            new_samp = np.random.multivariate_normal(mean_fitted_mod3,cov_mod3)[2]\n",
    "        sampled_parameters_mod3[i,2] = new_samp\n",
    "\n",
    "AIC_winner_datamod3 = np.zeros(100)\n",
    "BIC_winner_datamod3 = np.zeros(100)\n",
    "        \n",
    "for i in tqdm(range(100)):\n",
    "    simulated_cho_mod3 , simulated_out_mod3 , simulated_V_a_mod3 , simulated_V_b_mod3 = model3_simulate(np.array([sampled_parameters_mod3[i,0], sampled_parameters_mod3[i,1], sampled_parameters_mod3[i,2]]),0.5)\n",
    "    \n",
    "    #fit models to simulated data\n",
    "    optimized_datamod3_mod1 = sp.optimize.minimize(model1_neg_log_likelihood, theta_guess_mod1, args=(simulated_cho_mod3, simulated_out_mod3 ,0.5), method='Nelder-Mead').x\n",
    "    optimized_datamod3_mod2 = sp.optimize.minimize(model2_neg_log_likelihood, theta_guess_mod2, args=(simulated_cho_mod3, simulated_out_mod3 ,0.5), method='Nelder-Mead').x\n",
    "    optimized_datamod3_mod3 = sp.optimize.minimize(model3_neg_log_likelihood, theta_guess_mod3, args=(simulated_cho_mod3, simulated_out_mod3 ,0.5), method='Nelder-Mead').x\n",
    "    \n",
    "    #compute AIC and BIC scores for model 3\n",
    "    theta_nll_datamod3_mod1 = np.array([optimized_datamod3_mod1[0],optimized_datamod3_mod1[1]])\n",
    "    nll_datamod3_mod1 = model1_neg_log_likelihood(theta_nll_datamod3_mod1,simulated_cho_mod3,simulated_out_mod3 ,0.5)\n",
    "    AIC_datamod3_mod1 = 2*nll_datamod3_mod1 + 4 \n",
    "    BIC_datamod3_mod1 = 2*nll_datamod3_mod1 + 2*np.log(160)\n",
    "    \n",
    "    #compute AIC and BIC scores for model 3\n",
    "    theta_nll_datamod3_mod2 = np.array([optimized_datamod3_mod2[0],optimized_datamod3_mod2[1],optimized_datamod3_mod2[2]])\n",
    "    nll_datamod3_mod2 = model2_neg_log_likelihood(theta_nll_datamod3_mod2,simulated_cho_mod3,simulated_out_mod3 ,0.5)\n",
    "    AIC_datamod3_mod2 = 2*nll_datamod3_mod2 + 6 \n",
    "    BIC_datamod3_mod2 = 2*nll_datamod3_mod2 + 3*np.log(160)\n",
    "    \n",
    "    #compute AIC and BIC scores for model 3\n",
    "    theta_nll_datamod3_mod3 = np.array([optimized_datamod3_mod3[0],optimized_datamod3_mod3[1],optimized_datamod3_mod3[2]])\n",
    "    nll_datamod3_mod3 = model3_neg_log_likelihood(theta_nll_datamod2_mod3,simulated_cho_mod3,simulated_out_mod3 ,0.5)\n",
    "    AIC_datamod3_mod3 = 2*nll_datamod3_mod3 + 6 \n",
    "    BIC_datamod3_mod3 = 2*nll_datamod3_mod3 + 3*np.log(160)\n",
    "    \n",
    "    #Compare AICS:\n",
    "    AICs_datamod3 = np.array([AIC_datamod3_mod1,AIC_datamod3_mod2,AIC_datamod3_mod3])\n",
    "    AIC_winner_datamod3[i] = np.argmin(AICs_datamod3)\n",
    "    \n",
    "    #Compare BICS:\n",
    "    BICs_datamod3 = np.array([BIC_datamod3_mod1,BIC_datamod3_mod2,BIC_datamod3_mod3])\n",
    "    BIC_winner_datamod3[i] =np.argmin(BICs_datamod3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "desperate-subscription",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# AIC Confusion matrix \n",
    "\n",
    "AIC_matrix = np.zeros((3,3))\n",
    "\n",
    "AIC_matrix[0,0] = (len(np.where(AIC_winner_datamod1 == 0)[0])/len(AIC_winner_datamod1))*100\n",
    "AIC_matrix[0,1] = (len(np.where(AIC_winner_datamod1 == 1)[0])/len(AIC_winner_datamod1))*100\n",
    "AIC_matrix[0,2] = (len(np.where(AIC_winner_datamod1 == 2)[0])/len(AIC_winner_datamod1))*100\n",
    "\n",
    "AIC_matrix[1,0] = (len(np.where(AIC_winner_datamod2 == 0)[0])/len(AIC_winner_datamod2))*100\n",
    "AIC_matrix[1,1] = (len(np.where(AIC_winner_datamod2 == 1)[0])/len(AIC_winner_datamod2))*100\n",
    "AIC_matrix[1,2] = (len(np.where(AIC_winner_datamod2 == 2)[0])/len(AIC_winner_datamod2))*100\n",
    "\n",
    "AIC_matrix[2,0] = (len(np.where(AIC_winner_datamod3 == 0)[0])/len(AIC_winner_datamod3))*100\n",
    "AIC_matrix[2,1] = (len(np.where(AIC_winner_datamod3 == 1)[0])/len(AIC_winner_datamod3))*100\n",
    "AIC_matrix[2,2] = (len(np.where(AIC_winner_datamod3 == 2)[0])/len(AIC_winner_datamod3))*100\n",
    "\n",
    "\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "ax.matshow(AIC_matrix)\n",
    "for i in range(3):\n",
    "    for j in range(3):\n",
    "        plt.text(j, i, str(AIC_matrix[i, j]) + \"%\",\n",
    "                       ha=\"center\", va=\"center\", color=\"r\")\n",
    "ax.set_xticks(np.arange(3),np.array([1,2,3]))\n",
    "ax.set_yticks(np.arange(3),np.array([1,2,3]))       \n",
    "plt.xlabel(\"Best fitting model\",fontsize=12,**font)\n",
    "plt.ylabel(\"Model used to produce data set\",fontsize=12,**font)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "respected-presence",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# AIC Confusion matrix \n",
    "\n",
    "BIC_matrix = np.zeros((3,3))\n",
    "BIC_matrix[0,0] = (len(np.where(BIC_winner_datamod1 == 0)[0])/len(BIC_winner_datamod1))*100\n",
    "BIC_matrix[0,1] = (len(np.where(BIC_winner_datamod1 == 1)[0])/len(BIC_winner_datamod1))*100\n",
    "BIC_matrix[0,2] = (len(np.where(BIC_winner_datamod1 == 2)[0])/len(BIC_winner_datamod1))*100\n",
    "\n",
    "BIC_matrix[1,0] = (len(np.where(BIC_winner_datamod2 == 0)[0])/len(BIC_winner_datamod2))*100\n",
    "BIC_matrix[1,1] = (len(np.where(BIC_winner_datamod2 == 1)[0])/len(BIC_winner_datamod2))*100\n",
    "BIC_matrix[1,2] = (len(np.where(BIC_winner_datamod2 == 2)[0])/len(BIC_winner_datamod2))*100\n",
    "\n",
    "BIC_matrix[2,0] = (len(np.where(BIC_winner_datamod3 == 0)[0])/len(BIC_winner_datamod3))*100\n",
    "BIC_matrix[2,1] = (len(np.where(BIC_winner_datamod3 == 1)[0])/len(BIC_winner_datamod3))*100\n",
    "BIC_matrix[2,2] = (len(np.where(BIC_winner_datamod3 == 2)[0])/len(BIC_winner_datamod3))*100\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "ax.matshow(BIC_matrix)\n",
    "for i in range(3):\n",
    "    for j in range(3):\n",
    "        plt.text(j, i, str(int(BIC_matrix[i, j])) + \"%\",\n",
    "                       ha=\"center\", va=\"center\", color=\"r\")\n",
    "ax.set_xticks(np.arange(3),np.array([1,2,3]))\n",
    "ax.set_yticks(np.arange(3),np.array([1,2,3]))  \n",
    "plt.xlabel(\"Best fitting model\",fontsize=12,**font)\n",
    "plt.ylabel(\"Model used to produce data set\",fontsize=12,**font)\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}