C2/L4A_metropolis_hastings.ipynb

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    "import numpy as np\n",
    "import matplotlib.pyplot as plt \n",
    "import pandas as pd \n",
    "import seaborn as sns\n",
    "\n",
    "import sys\n",
    "sys.path.insert(0, '..')\n",
    "from utils.plot_lib import set_default\n",
    "\n",
    "set_default(figsize=(6, 4))"
   ]
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   "source": [
    "### Random walk with normal likelihood, $t$ prior\n",
    "\n",
    "Recall the model from the last segment of Lesson 2 where the data are the percent change in total personnel from last year to this year for $n=10$ companies. We used a normal likelihood with known variance and $t$ distribution for the prior on the unknown mean. Suppose the values are $y=(1.2,1.4,−0.5,0.3,0.9,2.3,1.0,0.1,1.3,1.9)$. Because this model is not conjugate, the posterior distribution is not in a standard form that we can easily sample. To obtain posterior samples, we will set up a Markov chain whose stationary distribution is this posterior distribution.\n",
    "\n",
    "$y_i | \\mu \\stackrel{iid}{\\sim} \\mathcal(\\mu, 1) \\text{ }i = 1, ..., n $\n",
    "\n",
    "$ \\mu \\sim t(0, 1, 1) $\n",
    "\n",
    "Recall that the posterior distribution is:\n",
    "\n",
    "$ p(\\mu \\mid y_1, \\ldots, y_n) \\propto \\frac{\\exp[ n ( \\bar{y} \\mu - \\mu^2/2)]}{1 + \\mu^2} $\n",
    "\n",
    "The posterior distribution on the left is our target distribution and the expression on the right is our $g(μ)$\n",
    "\n",
    "Because posterior distributions include likelihoods (the product of many numbers that are potentially small), $g(μ)$ might evaluate to such a small number that to the computer, it effectively zero. This will cause a problem when we evaluate the acceptance ratio $α$. To avoid this problem, we can work on the log scale, which will be more numerically stable. Thus, we will write a function to evaluate\n",
    "\n",
    "$ \\log(g(\\mu)) = n ( \\bar{y} \\mu - \\mu^2/2) - \\log(1 + \\mu^2) $\n",
    "\n",
    "Let's first write the log function."
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    "# Log function proportional to the posterior\n",
    "def log_function(mu, n, y_bar):\n",
    "    mu2 = mu**2\n",
    "    return n * (y_bar * mu - mu2 / 2.0) - np.log(1 + mu2)"
   ]
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  {
   "source": [
    "Random-Walk Metropolis-Hastings sampler with normal proposals."
   ],
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   "source": [
    "from scipy.stats import norm\n",
    "from scipy.stats import uniform\n",
    "\n",
    "def random_walk_sampler(n, y_bar, n_iter, mu_init, cand_sd):\n",
    "    ## Random-Walk Metropolis-Hastings algorithm\n",
    "\n",
    "    ## Step 1, initialize\n",
    "    mu_out = [] # Output vector\n",
    "    accpt = 0 # Number of samples accepted\n",
    "    mu_now = mu_init # Initial state\n",
    "    lg_now = log_function(mu = mu_now, n = n, y_bar = y_bar) # Current function value\n",
    "\n",
    "    ## Step 2, iterate\n",
    "    for i in range(n_iter):\n",
    "        ## Step 2a\n",
    "        mu_cand = norm.rvs(size=1, loc = mu_now, scale = cand_sd)[0] # draw a candidate\n",
    "\n",
    "        ## Step 2b\n",
    "        lg_cand = log_function(mu = mu_cand, n = n, y_bar = y_bar) # evaluate log of g with the candidate\n",
    "        lalpha = lg_cand - lg_now # log of acceptance ratio\n",
    "        alpha = np.exp(lalpha)\n",
    "\n",
    "        ## Step 2c\n",
    "        u = uniform.rvs(size = 1)[0] # draw a uniform variable which will be less than alpha with probability min(1, alpha)\n",
    "        if (u < alpha): # then accept the candidate\n",
    "            mu_now = mu_cand\n",
    "            accpt = accpt + 1 # to keep track of acceptance\n",
    "            lg_now = lg_cand\n",
    "\n",
    "        ## collect results\n",
    "        mu_out.append(mu_now) # save this iteration's value of mu\n",
    "\n",
    "    return mu_out, accpt / n_iter"
   ]
  },
  {
   "source": [
    "Setting the problem"
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\n"
     },
     "metadata": {}
    }
   ],
   "source": [
    "from scipy.stats import t\n",
    "\n",
    "y = np.array([1.2, 1.4, -0.5, 0.3, 0.9, 2.3, 1.0, 0.1, 1.3, 1.9]) # Data\n",
    "y_bar = np.mean(y) # Sample mean\n",
    "n = y.shape[0] # Data points\n",
    "\n",
    "# Plotting the histogram of the random samples\n",
    "fig, ax = plt.subplots(1, 1)\n",
    "sns.histplot(np.array(y), stat= 'density', bins = 6)\n",
    "# Sampling in all the domain of the function\n",
    "x = np.linspace(t.ppf(q = 0.01, df = 1),t.ppf(q = 0.99, df = 1), 100)\n",
    "ax.plot(np.sort(y), t.pdf(x = np.sort(y), df = 1), 'r-', lw=5, alpha=0.6, label='t Prior') # prior for mu \n",
    "ax.scatter(y, np.repeat(0, n), s = 30, c='green', label = 'Data points') # individual data points\n",
    "ax.scatter(y_bar, 0, s = 30, c='blue', label = 'Sample mean') # sample mean\n",
    "ax.legend(loc='best', frameon=False)\n",
    "plt.xlim(-1, 3)  \n",
    "plt.title('Histogram of data')\n",
    "plt.show()"
   ]
  },
  {
   "source": [
    "Run the sampler! Let’s use $m=1000$ iterations and proposal standard deviation (which controls the proposal step size) $3.0$, and initial value at the prior median $0$."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "The mean of the sampled distribution is: [0.7721997760340801, 0.7721997760340801, 0.7721997760340801, 0.7721997760340801, 0.7721997760340801]\nThe percentage of acceptance were: 0.116\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(43) # set the random seed for reproducibility\n",
    "it = int(1e3)\n",
    "samples, aceptance = random_walk_sampler(n = n, y_bar = y_bar, n_iter = it, mu_init = 0.0, cand_sd = 3.0)\n",
    "print('The mean of the sampled distribution is: {}'.format(samples[:5]))\n",
    "print('The percentage of acceptance were: {}'.format(aceptance))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
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     },
     "metadata": {}
    }
   ],
   "source": [
    "# Plotting the trace-plot\n",
    "fig, ax = plt.subplots(1, 1)\n",
    "ax.plot(np.arange(it), samples, 'r-', lw=3, alpha=0.6, label='Trace plot') # Trace plot of data\n",
    "ax.legend(loc='best', frameon=False)\n",
    "plt.title('Trace plot of data')\n",
    "plt.show()"
   ]
  },
  {
   "source": [
    "It shows the history of the chain and provides basic feedback about whether the chain has reached its stationary distribution.\n",
    "\n",
    "It appears our proposal step size was too large (acceptance rate below $23%$). Let’s try another."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "The mean of the sampled distribution is: [-0.07101312199363279, -0.13150806068918167, -0.16500276457357058, -0.16500276457357058, -0.13909634862464015]\nThe percentage of acceptance were: 0.942\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
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125.758734 82.42864 \nL 126.36807 77.797482 \nL 126.672739 77.886617 \nL 126.977407 73.484621 \nL 127.282075 81.934872 \nL 127.586744 84.843186 \nL 127.891412 85.074829 \nL 128.19608 93.149082 \nL 128.500749 95.621875 \nL 128.805417 99.546387 \nL 129.110085 100.337612 \nL 129.414754 89.746082 \nL 129.719422 85.771779 \nL 130.02409 85.10438 \nL 130.328758 77.407058 \nL 130.633427 77.531999 \nL 130.938095 81.611277 \nL 131.242763 77.876392 \nL 131.547432 85.320122 \nL 131.8521 85.939258 \nL 132.156768 94.802291 \nL 132.461437 92.278671 \nL 132.766105 103.12268 \nL 133.070773 104.426306 \nL 133.375441 92.659252 \nL 133.68011 99.301625 \nL 133.984778 99.744951 \nL 134.289446 95.938818 \nL 134.594115 87.834079 \nL 134.898783 91.991185 \nL 135.50812 104.890619 \nL 135.812788 107.119535 \nL 136.117456 107.635856 \nL 136.422125 110.737404 \nL 137.031461 101.713011 \nL 137.640798 106.350798 \nL 137.945466 105.227113 \nL 138.859471 121.648708 \nL 139.164139 128.513894 \nL 139.468808 127.095932 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     },
     "metadata": {}
    }
   ],
   "source": [
    "samples, aceptance = random_walk_sampler(n = n, y_bar = y_bar, n_iter = it, mu_init = 0.0, cand_sd = 0.05)\n",
    "print('The mean of the sampled distribution is: {}'.format(samples[:5]))\n",
    "print('The percentage of acceptance were: {}'.format(aceptance))\n",
    "\n",
    "# Plotting the trace-plot\n",
    "fig, ax = plt.subplots(1, 1)\n",
    "ax.plot(np.arange(it), samples, 'r-', lw=3, alpha=0.6, label='Trace plot') # Trace plot of data\n",
    "ax.legend(loc='best', frameon=False)\n",
    "plt.title('Trace plot of data')\n",
    "plt.show()"
   ]
  },
  {
   "source": [
    "The acceptance rate is too high (above $50%$). Let’s try something in between."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "The mean of the sampled distribution is: [1.406512956468385, 1.406512956468385, 1.3038891874131793, 1.1006790708210246, 0.7058252960154938]\nThe percentage of acceptance were: 0.371\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {}
    }
   ],
   "source": [
    "samples, aceptance = random_walk_sampler(n = n, y_bar = y_bar, n_iter = it, mu_init = 0.0, cand_sd = 0.9)\n",
    "print('The mean of the sampled distribution is: {}'.format(samples[:5]))\n",
    "print('The percentage of acceptance were: {}'.format(aceptance))\n",
    "\n",
    "# Plotting the trace-plot\n",
    "fig, ax = plt.subplots(1, 1)\n",
    "ax.plot(np.arange(it), samples, 'r-', lw=3, alpha=0.6, label='Trace plot') # Trace plot of data\n",
    "ax.legend(loc='best', frameon=False)\n",
    "plt.title('Trace plot of data')\n",
    "plt.show()"
   ]
  },
  {
   "source": [
    "The last one looks good!  let’s see what happens if we initialize the chain at some far-off value."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "The mean of the sampled distribution is: [29.73708290294415, 29.73708290294415, 29.73708290294415, 29.73708290294415, 28.98467782856045]\nThe percentage of acceptance were: 0.398\n"
     ]
    },
    {
     "output_type": "display_data",
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     },
     "metadata": {}
    }
   ],
   "source": [
    "samples, aceptance = random_walk_sampler(n = n, y_bar = y_bar, n_iter = it, mu_init = 30.0, cand_sd = 0.9)\n",
    "print('The mean of the sampled distribution is: {}'.format(samples[:5]))\n",
    "print('The percentage of acceptance were: {}'.format(aceptance))\n",
    "\n",
    "# Plotting the trace-plot\n",
    "fig, ax = plt.subplots(1, 1)\n",
    "ax.plot(np.arange(it), samples, 'r-', lw=3, alpha=0.6, label='Trace plot') # Trace plot of data\n",
    "ax.legend(loc='best', frameon=False)\n",
    "plt.title('Trace plot of data')\n",
    "plt.show()"
   ]
  },
  {
   "source": [
    "It took awhile to find the stationary distribution, but it looks like we succeeded! If we discard the first $100$ or so values, it appears like the rest of the samples come from the stationary distribution, our posterior distribution! Let’s plot the posterior density against the prior to see how the data updated our belief about $μ$."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {}
    }
   ],
   "source": [
    "samples_discard = samples[200:] # Discard the first 200 samples\n",
    "\n",
    "# Plotting the posterior density\n",
    "fig, ax = plt.subplots(1, 1)\n",
    "# Sampling in all the domain of the function\n",
    "x = np.linspace(-1 , 3, 100)\n",
    "ax.plot(x, t.pdf(x = x, df = 1), 'r-', lw = 3, alpha=0.6, label='t Prior') # prior for mu \n",
    "ax.scatter(y_bar, 0, s = 30, c='blue', label = 'Sample mean') # Sample mean\n",
    "# plot density estimate of the posterior\n",
    "sns.kdeplot(np.array(samples_discard), bw=0.5, label = 'Density estimate post')\n",
    "# Approximation true posterior\n",
    "ax.plot(x, 0.017*np.exp(log_function(mu = x, n = n, y_bar = y_bar)), 'b-', lw = 3, alpha=0.6, label='Approx true post')\n",
    "ax.legend(loc='upper right', frameon=False)\n",
    "plt.xlabel('mu')\n",
    "plt.title('Trace plot of data')\n",
    "plt.show()"
   ]
  },
  {
   "source": [
    "Obtaining posterior samples using the Metropolis-Hastings algorithm can be time-consuming and require some fine-tuning, as we’ve just seen. The good news is that we can rely on software to do most of the work for us."
   ],
   "cell_type": "markdown",
   "metadata": {}
  }
 ]
}