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Fix model notation
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tjburch committed Aug 22, 2020
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6 changes: 3 additions & 3 deletions riddler538_2020_Aug21/solution.ipynb
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"source": [
"We get what we would expect, a distribution bounded from 0-2. If both $p$ values are low or high, then 0 or 2 are favored. Otherwise, 1 is the most common. The distribution above shows that 0 is the most common, followed by 1, then 2, so we should expect both $p$ values to be relatively low (<0.5).\n",
"\n",
"Formalizing the model simple enough:\n",
"Formalizing the model is simple enough:\n",
"\n",
"\\begin{align*}\n",
" y_i &= \\text{PoissonBinomial}(\\mathbf{p})\\\\\n",
" p_i &= \\text{Uniform}(0,1)\\\\\n",
" y_i &~ \\text{PoissonBinomial}(\\mathbf{p})\\\\\n",
" p_i &~ \\text{Uniform}(0,1)\\\\\n",
"\\end{align*}\n",
"\n",
"Here I've claimed flat priors on $p_1$ and $p_2$. I do have a slight bias that they both should be low (mentioned above), but perhaps one is very, very low, and one is just above 0.5 - we should account for that possibility."
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