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@Shmuma
Shmuma committed May 21, 2022
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125 changes: 107 additions & 18 deletions 15-Chapter 15. Missing Data and Other Opportunities.ipynb
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"Code 15.21"
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"# 15.3 Categorical errors and discrete absences"
]
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"Code 15.29"
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"Random.seed!(9)\n",
"\n",
"N_houses = 100\n",
"α = 5\n",
"β = -3\n",
"k = 0.5\n",
"r = 0.2\n",
"\n",
"cat = rand(Bernoulli(k), N_houses)\n",
"notes = rand.([Poisson(α + β * c) for c ∈ cat])\n",
"R_C = rand(Bernoulli(r), N_houses)\n",
"\n",
"cat_obs = Vector{Int}(cat)\n",
"cat_obs[R_C] .= -9\n",
"\n",
"dat = (\n",
" notes = notes,\n",
" cat = cat_obs,\n",
" RC = R_C,\n",
" N = N_houses,\n",
");"
]
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"Code 15.30"
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"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 │ 1.55 0.0861 1.413 1.5511 1.6872 ▁▁▅█▅▁▁ │\n",
"│ b │ -0.2694 0.1358 -0.4872 -0.2687 -0.0541 ▁▁▁▂▄▇█▆▃▁▁▁ │\n",
"│ k │ 0.4639 0.0448 0.3926 0.4637 0.5344 ▁▂▇█▄▁▁ │\n",
"└───────┴──────────────────────────────────────────────────────────┘\n"
]
}
],
"source": [
"@model function m15_8(notes, cat, RC, N)\n",
" a ~ Normal()\n",
" b ~ Normal(0, 0.5)\n",
" k ~ Beta(2, 2)\n",
" λ = @. logistic(a + b * cat)\n",
" \n",
" for i ∈ eachindex(cat)\n",
" if !RC[i]\n",
" cat[i] ~ Bernoulli(k)\n",
" notes[i] ~ Poisson(λ[i])\n",
" else\n",
" Turing.@addlogprob! log(k) + poislogpdf(exp(a+b), notes[i])\n",
" Turing.@addlogprob! log(1-k) + poislogpdf(exp(a), notes[i])\n",
" end\n",
" end\n",
"end\n",
"\n",
"m15_8_ch = sample(m15_8(dat...), NUTS(), 10000)\n",
"m15_8_df = DataFrame(m15_8_ch)\n",
"precis(m15_8_df)"
]
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"id": "d0026c60",
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"metadata": {},
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"source": []
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105 changes: 105 additions & 0 deletions docs/15-Chapter 15. Missing Data and Other Opportunities.html
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Expand Up @@ -19129,6 +19129,111 @@ <h1 id="15.2-Missing-data">15.2 Missing data<a class="anchor-link" href="#15.2-M
<h1 id="15.3-Categorical-errors-and-discrete-absences">15.3 Categorical errors and discrete absences<a class="anchor-link" href="#15.3-Categorical-errors-and-discrete-absences">&#182;</a></h1>
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<p>Code 15.29</p>

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<div class=" highlight hl-julia"><pre><span></span><span class="n">Random</span><span class="o">.</span><span class="n">seed!</span><span class="p">(</span><span class="mi">9</span><span class="p">)</span>

<span class="n">N_houses</span> <span class="o">=</span> <span class="mi">100</span>
<span class="n">α</span> <span class="o">=</span> <span class="mi">5</span>
<span class="n">β</span> <span class="o">=</span> <span class="o">-</span><span class="mi">3</span>
<span class="n">k</span> <span class="o">=</span> <span class="mf">0.5</span>
<span class="n">r</span> <span class="o">=</span> <span class="mf">0.2</span>

<span class="n">cat</span> <span class="o">=</span> <span class="n">rand</span><span class="p">(</span><span class="n">Bernoulli</span><span class="p">(</span><span class="n">k</span><span class="p">),</span> <span class="n">N_houses</span><span class="p">)</span>
<span class="n">notes</span> <span class="o">=</span> <span class="n">rand</span><span class="o">.</span><span class="p">([</span><span class="n">Poisson</span><span class="p">(</span><span class="n">α</span> <span class="o">+</span> <span class="n">β</span> <span class="o">*</span> <span class="n">c</span><span class="p">)</span> <span class="k">for</span> <span class="n">c</span> <span class="o">∈</span> <span class="n">cat</span><span class="p">])</span>
<span class="n">R_C</span> <span class="o">=</span> <span class="n">rand</span><span class="p">(</span><span class="n">Bernoulli</span><span class="p">(</span><span class="n">r</span><span class="p">),</span> <span class="n">N_houses</span><span class="p">)</span>

<span class="n">cat_obs</span> <span class="o">=</span> <span class="kt">Vector</span><span class="p">{</span><span class="kt">Int</span><span class="p">}(</span><span class="n">cat</span><span class="p">)</span>
<span class="n">cat_obs</span><span class="p">[</span><span class="n">R_C</span><span class="p">]</span> <span class="o">.=</span> <span class="o">-</span><span class="mi">9</span>

<span class="n">dat</span> <span class="o">=</span> <span class="p">(</span>
<span class="n">notes</span> <span class="o">=</span> <span class="n">notes</span><span class="p">,</span>
<span class="n">cat</span> <span class="o">=</span> <span class="n">cat_obs</span><span class="p">,</span>
<span class="n">RC</span> <span class="o">=</span> <span class="n">R_C</span><span class="p">,</span>
<span class="n">N</span> <span class="o">=</span> <span class="n">N_houses</span><span class="p">,</span>
<span class="p">);</span>
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<p>Code 15.30</p>

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<div class=" highlight hl-julia"><pre><span></span><span class="nd">@model</span> <span class="k">function</span> <span class="n">m15_8</span><span class="p">(</span><span class="n">notes</span><span class="p">,</span> <span class="n">cat</span><span class="p">,</span> <span class="n">RC</span><span class="p">,</span> <span class="n">N</span><span class="p">)</span>
<span class="n">a</span> <span class="o">~</span> <span class="n">Normal</span><span class="p">()</span>
<span class="n">b</span> <span class="o">~</span> <span class="n">Normal</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">)</span>
<span class="n">k</span> <span class="o">~</span> <span class="n">Beta</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<span class="n">λ</span> <span class="o">=</span> <span class="nd">@.</span> <span class="n">logistic</span><span class="p">(</span><span class="n">a</span> <span class="o">+</span> <span class="n">b</span> <span class="o">*</span> <span class="n">cat</span><span class="p">)</span>

<span class="k">for</span> <span class="n">i</span> <span class="o">∈</span> <span class="n">eachindex</span><span class="p">(</span><span class="n">cat</span><span class="p">)</span>
<span class="k">if</span> <span class="o">!</span><span class="n">RC</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
<span class="n">cat</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">~</span> <span class="n">Bernoulli</span><span class="p">(</span><span class="n">k</span><span class="p">)</span>
<span class="n">notes</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">~</span> <span class="n">Poisson</span><span class="p">(</span><span class="n">λ</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
<span class="k">else</span>
<span class="n">Turing</span><span class="o">.</span><span class="nd">@addlogprob!</span> <span class="n">log</span><span class="p">(</span><span class="n">k</span><span class="p">)</span> <span class="o">+</span> <span class="n">poislogpdf</span><span class="p">(</span><span class="n">exp</span><span class="p">(</span><span class="n">a</span><span class="o">+</span><span class="n">b</span><span class="p">),</span> <span class="n">notes</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
<span class="n">Turing</span><span class="o">.</span><span class="nd">@addlogprob!</span> <span class="n">log</span><span class="p">(</span><span class="mi">1</span><span class="o">-</span><span class="n">k</span><span class="p">)</span> <span class="o">+</span> <span class="n">poislogpdf</span><span class="p">(</span><span class="n">exp</span><span class="p">(</span><span class="n">a</span><span class="p">),</span> <span class="n">notes</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
<span class="k">end</span>
<span class="k">end</span>
<span class="k">end</span>

<span class="n">m15_8_ch</span> <span class="o">=</span> <span class="n">sample</span><span class="p">(</span><span class="n">m15_8</span><span class="p">(</span><span class="n">dat</span><span class="o">...</span><span class="p">),</span> <span class="n">NUTS</span><span class="p">(),</span> <span class="mi">10000</span><span class="p">)</span>
<span class="n">m15_8_df</span> <span class="o">=</span> <span class="n">DataFrame</span><span class="p">(</span><span class="n">m15_8_ch</span><span class="p">)</span>
<span class="n">precis</span><span class="p">(</span><span class="n">m15_8_df</span><span class="p">)</span>
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<pre>┌───────┬──────────────────────────────────────────────────────────┐
│<span class="ansi-bold"> param </span>│<span class="ansi-bold"> mean </span><span class="ansi-bold"> std </span><span class="ansi-bold"> 5.5% </span><span class="ansi-bold"> 50% </span><span class="ansi-bold"> 94.5% </span><span class="ansi-bold"> histogram </span>│
├───────┼──────────────────────────────────────────────────────────┤
│ a │ 1.55 0.0861 1.413 1.5511 1.6872 ▁▁▅█▅▁▁ │
│ b │ -0.2694 0.1358 -0.4872 -0.2687 -0.0541 ▁▁▁▂▄▇█▆▃▁▁▁ │
│ k │ 0.4639 0.0448 0.3926 0.4637 0.5344 ▁▂▇█▄▁▁ │
└───────┴──────────────────────────────────────────────────────────┘
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