08-Chapter 8. Conditional Manatees.ipynb

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   "metadata": {},
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   "source": [
    "using CSV\n",
    "using Random\n",
    "using StatsBase\n",
    "using DataFrames\n",
    "using Turing\n",
    "using StatsPlots\n",
    "using StatsFuns\n",
    "using LaTeXStrings\n",
    "using StatisticalRethinking\n",
    "using StatisticalRethinking: link\n",
    "using StatisticalRethinkingPlots\n",
    "using ParetoSmooth\n",
    "using ParetoSmoothedImportanceSampling\n",
    "using Logging\n",
    "\n",
    "default(labels=false)\n",
    "Logging.disable_logging(Logging.Warn);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "22daac2a",
   "metadata": {},
   "source": [
    "# 8.1 Building an interaction"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "55db3b24",
   "metadata": {},
   "source": [
    "Code 8.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "764a873d",
   "metadata": {},
   "outputs": [],
   "source": [
    "d = DataFrame(CSV.File(\"data/rugged.csv\"))\n",
    "dd = d[completecases(d, :rgdppc_2000),:]\n",
    "dd[:,:log_gdp] = log.(dd.rgdppc_2000);\n",
    "dd[:,:log_gdp_std] = dd.log_gdp / mean(dd.log_gdp)\n",
    "dd[:,:rugged_std] = dd.rugged / maximum(dd.rugged);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2739bfcc",
   "metadata": {},
   "source": [
    "Code 8.2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "78535e95",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "model_m8_1 (generic function with 2 methods)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r̄ = mean(dd.rugged_std)\n",
    "\n",
    "@model function model_m8_1(rugged_std, log_gdp_std)\n",
    "    σ ~ Exponential()\n",
    "    a ~ Normal(1, 1)\n",
    "    b ~ Normal(0, 1)\n",
    "    μ = @. a + b * (rugged_std - r̄)\n",
    "    log_gdp_std ~ MvNormal(μ, σ)\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "43d8f814",
   "metadata": {},
   "source": [
    "Code 8.3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "c3a0786f",
   "metadata": {},
   "outputs": [],
   "source": [
    "m8_1_p = sample(model_m8_1(dd.rugged_std, dd.log_gdp_std), Prior(), 1000)\n",
    "m8_1_p_df = DataFrame(m8_1_p);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "2c27b14f",
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       "</svg>\n"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rugged_seq = range(-0.1, 1.1; length=30)\n",
    "μ = link(m8_1_p_df, (r, x) -> r.a + r.b*(x - r̄), rugged_seq)\n",
    "μ = hcat(μ...)\n",
    "\n",
    "p = plot(\n",
    "    xlim=(0, 1),\n",
    "    ylim=(0.5, 1.5),\n",
    "    title=L\"a \\sim \\mathcal{N}(1,1), b \\sim \\mathcal{N}(0, 1)\",\n",
    "    xlab=\"ruggedness\", ylab=\"log GDP\",\n",
    ")\n",
    "hline!(collect(extrema(dd.log_gdp_std)); c=:black, s=:dash)\n",
    "for μ₀ ∈ first(eachrow(μ), 50)\n",
    "    plot!(rugged_seq, μ₀; c=:black, alpha=0.3)\n",
    "end\n",
    "p"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e81fadaf",
   "metadata": {},
   "source": [
    "Code 8.4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "00ce89b5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.57"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean(abs.(m8_1_p_df.b) .> 0.6)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "18a6912b",
   "metadata": {},
   "source": [
    "Code 8.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "9d8d0f94",
   "metadata": {},
   "outputs": [],
   "source": [
    "r̄ = mean(dd.rugged_std)\n",
    "\n",
    "@model function model_m8_1a(rugged_std, log_gdp_std)\n",
    "    σ ~ Exponential()\n",
    "    a ~ Normal(1, 0.1)\n",
    "    b ~ Normal(0, 0.3)\n",
    "    μ = @. a + b * (rugged_std - r̄)\n",
    "    log_gdp_std ~ MvNormal(μ, σ)\n",
    "end\n",
    "\n",
    "m8_1 = sample(model_m8_1a(dd.rugged_std, dd.log_gdp_std), NUTS(), 1000)\n",
    "m8_1_df = DataFrame(m8_1);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6b0d95a2",
   "metadata": {},
   "source": [
    "Code 8.6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "f5da06a9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "┌───────┬──────────────────────────────────────────────────────┐\n",
      "│\u001b[1m param \u001b[0m│\u001b[1m   mean \u001b[0m\u001b[1m    std \u001b[0m\u001b[1m    5.5% \u001b[0m\u001b[1m    50% \u001b[0m\u001b[1m  94.5% \u001b[0m\u001b[1m   histogram \u001b[0m│\n",
      "├───────┼──────────────────────────────────────────────────────┤\n",
      "│     a │ 0.9997  0.0111   0.9826  0.9992  1.0168     ▁▁▄█▇▅▁▁ │\n",
      "│     b │ 0.0001  0.0563  -0.0912   0.001  0.0864    ▁▁▅██▅▁▁▁ │\n",
      "│     σ │ 0.1387  0.0075   0.1271  0.1384  0.1509  ▁▁▃██▇▅▂▁▁▁ │\n",
      "└───────┴──────────────────────────────────────────────────────┘\n"
     ]
    }
   ],
   "source": [
    "precis(m8_1_df)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cabbc1e5",
   "metadata": {},
   "source": [
    "Code 8.7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "8f1db6b2",
   "metadata": {},
   "outputs": [],
   "source": [
    "dd[:,:cid] = @. ifelse(dd.cont_africa == 1, 1, 2);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "62a9bf04",
   "metadata": {},
   "source": [
    "Code 8.8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "8ff42410",
   "metadata": {},
   "outputs": [],
   "source": [
    "@model function model_m8_2(rugged_std, cid,  log_gdp_std)\n",
    "    σ ~ Exponential()\n",
    "    a ~ MvNormal([1, 1], 0.1)\n",
    "    b ~ Normal(0, 0.3)\n",
    "    μ = @. a[cid] + b * (rugged_std - r̄)\n",
    "    log_gdp_std ~ MvNormal(μ, σ)\n",
    "end\n",
    "\n",
    "m8_2 = sample(model_m8_2(dd.rugged_std, dd.cid,  dd.log_gdp_std), NUTS(), 1000)\n",
    "m8_2_df = DataFrame(m8_2);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b14c893b",
   "metadata": {},
   "source": [
    "Code 8.9"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "f061509a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div class=\"data-frame\"><p>2 rows × 8 columns</p><table class=\"data-frame\"><thead><tr><th></th><th>models</th><th>WAIC</th><th>lppd</th><th>SE</th><th>dWAIC</th><th>dSE</th><th>pWAIC</th><th>weight</th></tr><tr><th></th><th title=\"String\">String</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th></tr></thead><tbody><tr><th>1</th><td>m8.2</td><td>-252.0</td><td>-260.56</td><td>14.82</td><td>0.0</td><td>0.0</td><td>4.27</td><td>1.0</td></tr><tr><th>2</th><td>m8.1</td><td>-188.8</td><td>-193.98</td><td>12.87</td><td>63.2</td><td>14.67</td><td>2.6</td><td>0.0</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cccccccc}\n",
       "\t& models & WAIC & lppd & SE & dWAIC & dSE & pWAIC & weight\\\\\n",
       "\t\\hline\n",
       "\t& String & Float64 & Float64 & Float64 & Float64 & Float64 & Float64 & Float64\\\\\n",
       "\t\\hline\n",
       "\t1 & m8.2 & -252.0 & -260.56 & 14.82 & 0.0 & 0.0 & 4.27 & 1.0 \\\\\n",
       "\t2 & m8.1 & -188.8 & -193.98 & 12.87 & 63.2 & 14.67 & 2.6 & 0.0 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m2×8 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m models \u001b[0m\u001b[1m WAIC    \u001b[0m\u001b[1m lppd    \u001b[0m\u001b[1m SE      \u001b[0m\u001b[1m dWAIC   \u001b[0m\u001b[1m dSE     \u001b[0m\u001b[1m pWAIC   \u001b[0m\u001b[1m weight  \u001b[0m\n",
       "\u001b[1m     \u001b[0m│\u001b[90m String \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\n",
       "─────┼───────────────────────────────────────────────────────────────────────\n",
       "   1 │ m8.2     -252.0  -260.56    14.82      0.0     0.0      4.27      1.0\n",
       "   2 │ m8.1     -188.8  -193.98    12.87     63.2    14.67     2.6       0.0"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Compute log likelihoods for both models\n",
    "fun = (r, (x,y)) -> normlogpdf(r.a + r.b * (x - r̄), r.σ, y)\n",
    "m8_1_ll = link(m8_1_df, fun, zip(dd.rugged_std, dd.log_gdp_std))\n",
    "m8_1_ll = hcat(m8_1_ll...)\n",
    "\n",
    "# need DF with a as a vector of both a[1] and a[2]\n",
    "df = DataFrame(m8_2_df)\n",
    "df[!,:a] = collect.(zip(m8_2_df.:\"a[1]\", m8_2_df.:\"a[2]\"))\n",
    "\n",
    "fun = (r, (x,c,y)) -> normlogpdf(r.a[c] + r.b * (x - r̄), r.σ, y)\n",
    "m8_2_ll = link(df, fun, zip(dd.rugged_std, dd.cid, dd.log_gdp_std))\n",
    "m8_2_ll = hcat(m8_2_ll...);\n",
    "\n",
    "compare([m8_1_ll, m8_2_ll], :waic, mnames=[\"m8.1\", \"m8.2\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "71579cab",
   "metadata": {},
   "source": [
    "Code 8.10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "9938208c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "┌───────┬────────────────────────────────────────────────────────────┐\n",
      "│\u001b[1m param \u001b[0m│\u001b[1m    mean \u001b[0m\u001b[1m    std \u001b[0m\u001b[1m    5.5% \u001b[0m\u001b[1m     50% \u001b[0m\u001b[1m  94.5% \u001b[0m\u001b[1m       histogram \u001b[0m│\n",
      "├───────┼────────────────────────────────────────────────────────────┤\n",
      "│  a[1] │  0.8808  0.0164   0.8546    0.881  0.9061      ▁▁▃▆██▇▃▁▁▁ │\n",
      "│  a[2] │  1.0494  0.0102   1.0336   1.0494  1.0656  ▁▁▁▁▂▅▆██▆▄▂▁▁▁ │\n",
      "│     b │ -0.0457   0.049  -0.1251  -0.0453  0.0324          ▁▁▃██▄▁ │\n",
      "│     σ │  0.1143  0.0064   0.1043   0.1141  0.1253         ▁▂▅█▇▃▂▁ │\n",
      "└───────┴────────────────────────────────────────────────────────────┘\n"
     ]
    }
   ],
   "source": [
    "precis(m8_2_df)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ae7e5138",
   "metadata": {},
   "source": [
    "Code 8.11"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "c342d494",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Vector{Float64}:\n",
       " -0.19825561525781646\n",
       " -0.13851770975439429"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "PI(map(r -> r[1] - r[2], df.a))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ef834e40",
   "metadata": {},
   "source": [
    "Code 8.12"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "cfe922de",
   "metadata": {},
   "outputs": [],
   "source": [
    "rugged_seq = range(-0.1, 1.1, length=30)\n",
    "africa     = link(df, (r, x) -> r.a[1] + r.b*(x-r̄), rugged_seq)\n",
    "africa     = hcat(africa...)'\n",
    "not_africa = link(df, (r, x) -> r.a[2] + r.b*(x-r̄), rugged_seq)\n",
    "not_africa = hcat(not_africa...)'\n",
    "\n",
    "μₐ = mean.(eachrow(africa))\n",
    "μₙ = mean.(eachrow(not_africa))\n",
    "PIₐ = PI.(eachrow(africa))\n",
    "PIₐ = vcat(PIₐ'...)\n",
    "PIₙ = PI.(eachrow(not_africa))\n",
    "PIₙ = vcat(PIₙ'...);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "d4f96766",
   "metadata": {},
   "outputs": [
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      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p = plot(xlab=\"ruggedness (std)\", ylab=\"log GDP\")\n",
    "scatter!(dd.rugged_std[dd.cid.==1], dd.log_gdp_std[dd.cid.==1], c=:blue)\n",
    "scatter!(dd.rugged_std[dd.cid.==2], dd.log_gdp_std[dd.cid.==2], c=:white)\n",
    "\n",
    "plot!(rugged_seq, [μₐ, μₐ], c=:black, fillrange=PIₐ, fillalpha=0.4)\n",
    "plot!(rugged_seq, [μₙ, μₙ], c=:black, fillrange=PIₙ, fillalpha=0.2)\n",
    "annotate!([\n",
    "    (1, 0.87, (\"Africa\", 9)),\n",
    "    (1, 1.05, (\"Not Africa\", 9))\n",
    "])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "91816e85",
   "metadata": {},
   "source": [
    "Code 8.13"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "f21f998c",
   "metadata": {},
   "outputs": [],
   "source": [
    "@model function model_m8_3(rugged_std, cid,  log_gdp_std)\n",
    "    σ ~ Exponential()\n",
    "    a ~ MvNormal([1, 1], 0.1)\n",
    "    b ~ MvNormal([0, 0], 0.3)\n",
    "    μ = @. a[cid] + b[cid] * (rugged_std - r̄)\n",
    "    log_gdp_std ~ MvNormal(μ, σ)\n",
    "end\n",
    "\n",
    "m8_3 = sample(model_m8_3(dd.rugged_std, dd.cid,  dd.log_gdp_std), NUTS(), 1000)\n",
    "m8_3_df = DataFrame(m8_3);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c7ff59c4",
   "metadata": {},
   "source": [
    "Code 8.14"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "78c7c329",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "┌───────┬──────────────────────────────────────────────────────────┐\n",
      "│\u001b[1m param \u001b[0m│\u001b[1m    mean \u001b[0m\u001b[1m    std \u001b[0m\u001b[1m   5.5% \u001b[0m\u001b[1m     50% \u001b[0m\u001b[1m   94.5% \u001b[0m\u001b[1m     histogram \u001b[0m│\n",
      "├───────┼──────────────────────────────────────────────────────────┤\n",
      "│  a[1] │  0.8873  0.0158  0.8635   0.8876   0.9123   ▁▁▁▂▄▇██▅▂▁▁ │\n",
      "│  a[2] │   1.051  0.0102  1.0348   1.0509   1.0676  ▁▁▂▄▆██▆▅▃▁▁▁ │\n",
      "│  b[1] │  0.1301  0.0754  0.0068   0.1318   0.2486    ▁▁▃▆█▇▄▂▁▁▁ │\n",
      "│  b[2] │ -0.1399  0.0561  -0.231  -0.1404  -0.0515        ▁▃██▅▂▁ │\n",
      "│     σ │  0.1114  0.0063  0.1019   0.1111   0.1223       ▁▄██▆▃▁▁ │\n",
      "└───────┴──────────────────────────────────────────────────────────┘\n"
     ]
    }
   ],
   "source": [
    "precis(m8_3_df)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6ce88c91",
   "metadata": {},
   "source": [
    "Code 8.15"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "0033be97",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<div class=\"data-frame\"><p>3 rows × 8 columns</p><table class=\"data-frame\"><thead><tr><th></th><th>models</th><th>PSIS</th><th>lppd</th><th>SE</th><th>dPSIS</th><th>dSE</th><th>pPSIS</th><th>weight</th></tr><tr><th></th><th title=\"String\">String</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th></tr></thead><tbody><tr><th>1</th><td>m8.3</td><td>-259.9</td><td>-269.18</td><td>14.56</td><td>0.0</td><td>0.0</td><td>5.02</td><td>0.98</td></tr><tr><th>2</th><td>m8.2</td><td>-252.5</td><td>-260.56</td><td>14.75</td><td>7.4</td><td>6.38</td><td>4.27</td><td>0.02</td></tr><tr><th>3</th><td>m8.1</td><td>-189.1</td><td>-193.98</td><td>12.84</td><td>70.8</td><td>14.77</td><td>2.6</td><td>0.0</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cccccccc}\n",
       "\t& models & PSIS & lppd & SE & dPSIS & dSE & pPSIS & weight\\\\\n",
       "\t\\hline\n",
       "\t& String & Float64 & Float64 & Float64 & Float64 & Float64 & Float64 & Float64\\\\\n",
       "\t\\hline\n",
       "\t1 & m8.3 & -259.9 & -269.18 & 14.56 & 0.0 & 0.0 & 5.02 & 0.98 \\\\\n",
       "\t2 & m8.2 & -252.5 & -260.56 & 14.75 & 7.4 & 6.38 & 4.27 & 0.02 \\\\\n",
       "\t3 & m8.1 & -189.1 & -193.98 & 12.84 & 70.8 & 14.77 & 2.6 & 0.0 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m3×8 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m models \u001b[0m\u001b[1m PSIS    \u001b[0m\u001b[1m lppd    \u001b[0m\u001b[1m SE      \u001b[0m\u001b[1m dPSIS   \u001b[0m\u001b[1m dSE     \u001b[0m\u001b[1m pPSIS   \u001b[0m\u001b[1m weight  \u001b[0m\n",
       "\u001b[1m     \u001b[0m│\u001b[90m String \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\n",
       "─────┼───────────────────────────────────────────────────────────────────────\n",
       "   1 │ m8.3     -259.9  -269.18    14.56      0.0     0.0      5.02     0.98\n",
       "   2 │ m8.2     -252.5  -260.56    14.75      7.4     6.38     4.27     0.02\n",
       "   3 │ m8.1     -189.1  -193.98    12.84     70.8    14.77     2.6      0.0"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df3 = DataFrame(m8_3_df)\n",
    "df3[!,:a] = collect.(zip(m8_3_df.:\"a[1]\", m8_3_df.:\"a[2]\"))\n",
    "df3[!,:b] = collect.(zip(m8_3_df.:\"b[1]\", m8_3_df.:\"b[2]\"))\n",
    "\n",
    "fun = (r, (x,c,y)) -> normlogpdf(r.a[c] + r.b[c] * (x - r̄), r.σ, y)\n",
    "m8_3_ll = link(df3, fun, zip(dd.rugged_std, dd.cid, dd.log_gdp_std))\n",
    "m8_3_ll = hcat(m8_3_ll...);\n",
    "\n",
    "compare([m8_1_ll, m8_2_ll, m8_3_ll], :psis, mnames=[\"m8.1\", \"m8.2\", \"m8.3\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7c8cde5f",
   "metadata": {},
   "source": [
    "Code 8.16"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "9d987800",
   "metadata": {},
   "outputs": [
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     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t = m8_3_ll'\n",
    "m8_3_t = collect(reshape(t, size(t)..., 1))\n",
    "PSIS_m8_3 = psis_loo(m8_3_t)\n",
    "scatter(PSIS_m8_3.pointwise(:pareto_k))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "93ec77b8",
   "metadata": {},
   "source": [
    "Code 8.17"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "bd6e1107",
   "metadata": {},
   "outputs": [
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     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# build data\n",
    "africa     = link(df3, (r, x) -> r.a[1] + r.b[1]*(x-r̄), rugged_seq)\n",
    "africa     = hcat(africa...)'\n",
    "not_africa = link(df3, (r, x) -> r.a[2] + r.b[2]*(x-r̄), rugged_seq)\n",
    "not_africa = hcat(not_africa...)'\n",
    "\n",
    "μₐ = mean.(eachrow(africa))\n",
    "μₙ = mean.(eachrow(not_africa))\n",
    "PIₐ = PI.(eachrow(africa))\n",
    "PIₐ = vcat(PIₐ'...)\n",
    "PIₙ = PI.(eachrow(not_africa))\n",
    "PIₙ = vcat(PIₙ'...);\n",
    "\n",
    "# plot Africa, cid=1\n",
    "p1 = plot(xlab=\"ruggedness (std)\", ylab=\"log GDP\", title=\"African nations\")\n",
    "scatter!(dd.rugged_std[dd.cid.==1], dd.log_gdp_std[dd.cid.==1], c=:blue)\n",
    "plot!(rugged_seq, [μₐ, μₐ], c=:blue, fillrange=PIₐ, fillalpha=0.2)\n",
    "\n",
    "# plot non Africa, cid=2\n",
    "p2 = plot(xlab=\"ruggedness (std)\", ylab=\"log GDP\", title=\"Non-African nations\")\n",
    "scatter!(dd.rugged_std[dd.cid.==2], dd.log_gdp_std[dd.cid.==2], c=:white)\n",
    "plot!(rugged_seq, [μₙ, μₙ], c=:black, fillrange=PIₙ, fillalpha=0.2)\n",
    "\n",
    "plot(p1, p2, size=(800, 400))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "81c08bbf",
   "metadata": {},
   "source": [
    "# 8.2 Symmetry of interations"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d2d5f3df",
   "metadata": {},
   "source": [
    "Code 8.18"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "f346fbc6",
   "metadata": {},
   "outputs": [],
   "source": [
    "rugged_seq = range(-0.2, 1.2, length=30)\n",
    "μA = link(df3, (r, x) -> r.a[1] + r.b[1]*(x-r̄), rugged_seq)\n",
    "μA = vcat(μA'...)\n",
    "μN = link(df3, (r, x) -> r.a[2] + r.b[2]*(x-r̄), rugged_seq)\n",
    "μN = vcat(μN'...)\n",
    "delta = μA .- μN;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "45c8bb35",
   "metadata": {},
   "outputs": [
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      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "μ = mean.(eachrow(delta))\n",
    "PI_v = PI.(eachrow(delta))\n",
    "PI_v = vcat(PI_v'...)\n",
    "\n",
    "plot(xlab=\"ruggedness\", ylab=\"expected difference log GDP\",)\n",
    "plot!(rugged_seq, [μ, μ], c=:blue, fillrange=PI_v, fillalpha=0.2)\n",
    "hline!([0.0], s=:dash, c=:black)\n",
    "annotate!([\n",
    "    (0.0, 0.03, (\"Africa higher GPD\", 10)),\n",
    "    (0.0, -0.03, (\"Africa lower GPD\", 10)),\n",
    "])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "80a2beaf",
   "metadata": {},
   "source": [
    "# 8.3 Continuous interaction"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ad07a1b9",
   "metadata": {},
   "source": [
    "Code 8.19"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "a9284dc2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div class=\"data-frame\"><p>4 rows × 7 columns</p><table class=\"data-frame\"><thead><tr><th></th><th>variable</th><th>mean</th><th>min</th><th>median</th><th>max</th><th>nmissing</th><th>eltype</th></tr><tr><th></th><th title=\"Symbol\">Symbol</th><th title=\"Union{Nothing, Float64}\">Union…</th><th title=\"Any\">Any</th><th title=\"Union{Nothing, Float64}\">Union…</th><th title=\"Any\">Any</th><th title=\"Int64\">Int64</th><th title=\"DataType\">DataType</th></tr></thead><tbody><tr><th>1</th><td>bed</td><td></td><td>a</td><td></td><td>c</td><td>0</td><td>String1</td></tr><tr><th>2</th><td>water</td><td>2.0</td><td>1</td><td>2.0</td><td>3</td><td>0</td><td>Int64</td></tr><tr><th>3</th><td>shade</td><td>2.0</td><td>1</td><td>2.0</td><td>3</td><td>0</td><td>Int64</td></tr><tr><th>4</th><td>blooms</td><td>128.994</td><td>0.0</td><td>111.04</td><td>361.66</td><td>0</td><td>Float64</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccccccc}\n",
       "\t& variable & mean & min & median & max & nmissing & eltype\\\\\n",
       "\t\\hline\n",
       "\t& Symbol & Union… & Any & Union… & Any & Int64 & DataType\\\\\n",
       "\t\\hline\n",
       "\t1 & bed &  & a &  & c & 0 & String1 \\\\\n",
       "\t2 & water & 2.0 & 1 & 2.0 & 3 & 0 & Int64 \\\\\n",
       "\t3 & shade & 2.0 & 1 & 2.0 & 3 & 0 & Int64 \\\\\n",
       "\t4 & blooms & 128.994 & 0.0 & 111.04 & 361.66 & 0 & Float64 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m4×7 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m variable \u001b[0m\u001b[1m mean    \u001b[0m\u001b[1m min \u001b[0m\u001b[1m median \u001b[0m\u001b[1m max    \u001b[0m\u001b[1m nmissing \u001b[0m\u001b[1m eltype   \u001b[0m\n",
       "\u001b[1m     \u001b[0m│\u001b[90m Symbol   \u001b[0m\u001b[90m Union…  \u001b[0m\u001b[90m Any \u001b[0m\u001b[90m Union… \u001b[0m\u001b[90m Any    \u001b[0m\u001b[90m Int64    \u001b[0m\u001b[90m DataType \u001b[0m\n",
       "─────┼────────────────────────────────────────────────────────────\n",
       "   1 │ bed      \u001b[90m         \u001b[0m a   \u001b[90m        \u001b[0m c              0  String1\n",
       "   2 │ water     2.0      1    2.0     3              0  Int64\n",
       "   3 │ shade     2.0      1    2.0     3              0  Int64\n",
       "   4 │ blooms    128.994  0.0  111.04  361.66         0  Float64"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d = DataFrame(CSV.File(\"data/tulips.csv\"))\n",
    "describe(d)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a4bfaa4f",
   "metadata": {},
   "source": [
    "Code 8.20"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "6a33b4cb",
   "metadata": {},
   "outputs": [],
   "source": [
    "d.blooms_std = d.blooms / maximum(d.blooms)\n",
    "d.water_cent = d.water .- mean(d.water)\n",
    "d.shade_cent = d.shade .- mean(d.shade);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dfd67410",
   "metadata": {},
   "source": [
    "Code 8.21"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "eda60514",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6176"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Random.seed!(1)\n",
    "a = rand(Normal(0.5, 1), 10^4)\n",
    "sum(@. (a < 0) | (a > 1))/length(a)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2803842d",
   "metadata": {},
   "source": [
    "Code 8.22"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "47a89f28",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0469"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Random.seed!(1)\n",
    "a = rand(Normal(0.5, 0.25), 10^4)\n",
    "sum(@. (a < 0) | (a > 1))/length(a)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3d883ed1",
   "metadata": {},
   "source": [
    "Code 8.23"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "717b2020",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "┌───────┬──────────────────────────────────────────────────────────┐\n",
      "│\u001b[1m param \u001b[0m│\u001b[1m    mean \u001b[0m\u001b[1m    std \u001b[0m\u001b[1m    5.5% \u001b[0m\u001b[1m     50% \u001b[0m\u001b[1m   94.5% \u001b[0m\u001b[1m    histogram \u001b[0m│\n",
      "├───────┼──────────────────────────────────────────────────────────┤\n",
      "│     a │    0.36  0.0344   0.3067   0.3596   0.4167   ▁▁▂▃▆██▅▄▂▁ │\n",
      "│    bs │ -0.1111  0.0412  -0.1747  -0.1104  -0.0476       ▁▁▃█▆▂▁ │\n",
      "│    bw │  0.2034  0.0414     0.14    0.203   0.2721       ▁▁▂██▃▁ │\n",
      "│     σ │  0.1781  0.0291   0.1398   0.1741   0.2299  ▁▂▇█▆▄▂▁▁▁▁▁ │\n",
      "└───────┴──────────────────────────────────────────────────────────┘\n"
     ]
    }
   ],
   "source": [
    "@model function m8_4(water_cent, shade_cent, blooms_std)\n",
    "    a ~ Normal(0.5, 0.25)\n",
    "    bw ~ Normal(0, 0.25)\n",
    "    bs ~ Normal(0, 0.25)\n",
    "    μ = @. a + bw*water_cent + bs*shade_cent\n",
    "    σ ~ Exponential(1)\n",
    "    blooms_std ~ MvNormal(μ, σ)\n",
    "end\n",
    "\n",
    "m8_4_c = sample(m8_4(d.water_cent, d.shade_cent, d.blooms_std), NUTS(), 1000)\n",
    "m8_4_df = DataFrame(m8_4_c)\n",
    "precis(m8_4_df)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a7d4c0b2",
   "metadata": {},
   "source": [
    "Code 8.24"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "d91416a8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "┌───────┬───────────────────────────────────────────────────────────┐\n",
      "│\u001b[1m param \u001b[0m│\u001b[1m    mean \u001b[0m\u001b[1m    std \u001b[0m\u001b[1m    5.5% \u001b[0m\u001b[1m     50% \u001b[0m\u001b[1m   94.5% \u001b[0m\u001b[1m     histogram \u001b[0m│\n",
      "├───────┼───────────────────────────────────────────────────────────┤\n",
      "│     a │  0.3576  0.0286   0.3136   0.3586   0.4017  ▁▁▁▂▅██▄▂▁▁▁▁ │\n",
      "│    bs │ -0.1131  0.0331  -0.1658  -0.1136  -0.0622  ▁▁▁▂▄▇█▇▃▂▁▁▁ │\n",
      "│    bw │  0.2071  0.0334   0.1554   0.2064   0.2613         ▁▁▆█▂▁ │\n",
      "│   bws │ -0.1404  0.0405  -0.2043  -0.1391  -0.0763         ▁▁▆█▃▁ │\n",
      "│     σ │   0.142  0.0217   0.1121   0.1394   0.1777      ▁▄█▇▃▁▁▁▁ │\n",
      "└───────┴───────────────────────────────────────────────────────────┘\n"
     ]
    }
   ],
   "source": [
    "@model function m8_5(water_cent, shade_cent, blooms_std)\n",
    "    a ~ Normal(0.5, 0.25)\n",
    "    bw ~ Normal(0, 0.25)\n",
    "    bs ~ Normal(0, 0.25)\n",
    "    bws ~ Normal(0, 0.25)\n",
    "    μ = @. a + bw*water_cent + bs*shade_cent + bws*water_cent*shade_cent\n",
    "    σ ~ Exponential(1)\n",
    "    blooms_std ~ MvNormal(μ, σ)\n",
    "end\n",
    "\n",
    "m8_5_c = sample(m8_5(d.water_cent, d.shade_cent, d.blooms_std), NUTS(), 1000)\n",
    "m8_5_df = DataFrame(m8_5_c)\n",
    "precis(m8_5_df)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cee4417b",
   "metadata": {},
   "source": [
    "Code 8.25"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "46b8e617",
   "metadata": {},
   "outputs": [
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     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plts = []\n",
    "\n",
    "for shade ∈ -1:1\n",
    "    idx = findall(==(shade), d.shade_cent)\n",
    "    p = plot(xlims=(-1.2,1.2), ylims=(-.2,1.2), xlab=\"water\", ylab=\"blooms\", \n",
    "             title=\"shade=$shade\", titlefontsize=12)\n",
    "    scatter!(d.water_cent[idx], d.blooms_std[idx])\n",
    "    water_seq = -1:1\n",
    "    mu = link(m8_4_df, (r, water) -> r.a + r.bw * water + r.bs * shade, water_seq)\n",
    "    mu = hcat(mu...);\n",
    "    for μ ∈ first(eachrow(mu), 20)\n",
    "        plot!(water_seq, μ, c=:black, alpha=0.2)\n",
    "    end\n",
    "    push!(plts, p)\n",
    "end\n",
    "plot(plts..., layout=(1, 3), size=(800, 400), plot_title=\"m8.4 post\", plot_titlefontsize=14)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "7386cc0c",
   "metadata": {},
   "outputs": [
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     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plts = []\n",
    "\n",
    "for shade ∈ -1:1\n",
    "    idx = findall(==(shade), d.shade_cent)\n",
    "    p = plot(xlims=(-1.2,1.2), ylims=(-.2,1.2), xlab=\"water\", ylab=\"blooms\", \n",
    "             title=\"shade=$shade\", titlefontsize=12)\n",
    "    scatter!(d.water_cent[idx], d.blooms_std[idx])\n",
    "    water_seq = -1:1\n",
    "    mu = link(m8_5_df, (r, water) -> r.a + r.bw*water + r.bs*shade + r.bws*water*shade, water_seq)\n",
    "    mu = hcat(mu...);\n",
    "    for μ ∈ first(eachrow(mu), 20)\n",
    "        plot!(water_seq, μ, c=:black, alpha=0.2)\n",
    "    end\n",
    "    push!(plts, p)\n",
    "end\n",
    "plot(plts..., layout=(1, 3), size=(800, 400), plot_title=\"m8.5 post\", plot_titlefontsize=14)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "98db0780",
   "metadata": {},
   "source": [
    "Code 8.26"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "fa301fa2",
   "metadata": {},
   "outputs": [],
   "source": [
    "Random.seed!(7)\n",
    "m8_5p_c = sample(m8_5(d.water_cent, d.shade_cent, d.blooms_std), Prior(), 1000)\n",
    "m8_5p_df = DataFrame(m8_5p_c);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "9f0306f6",
   "metadata": {},
   "outputs": [
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      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plts = []\n",
    "\n",
    "for shade ∈ -1:1\n",
    "    p = plot(xlims=(-1, 1), ylims=(-0.5, 1.5), xlab=\"water\", ylab=\"blooms\", \n",
    "             title=\"shade=$shade\", titlefontsize=12)\n",
    "    water_seq = -1:1\n",
    "    mu = link(m8_5p_df, (r, water) -> r.a + r.bw*water + r.bs*shade + r.bws*water*shade, water_seq)\n",
    "    mu = hcat(mu...);\n",
    "    for μ ∈ first(eachrow(mu), 20)\n",
    "        plot!(water_seq, μ, c=:black, alpha=0.2)\n",
    "    end\n",
    "    hline!([0.0, 1.0], s=:dash, c=:black)\n",
    "    push!(plts, p)\n",
    "end\n",
    "plot(plts..., layout=(1, 3), size=(800, 400), plot_title=\"m8.5 prior\", plot_titlefontsize=14)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "48596a35",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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