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minor updates
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elizavetasemenova committed Nov 27, 2024
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74 changes: 37 additions & 37 deletions 04_probability_distributions.ipynb
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7 changes: 6 additions & 1 deletion 06_Monte_Carlo.ipynb
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"\\hat{\\mathbb{E}} (\\theta |x) = \\frac{1}{M} \\sum_{m=1}^M \\theta^{(m)}, \\quad \\theta^{(m)} \\sim p(\\theta|x).\n",
"$$\n",
"\n",
"This approach is called <font color='orange'>Monte Carlo integration</font> and avoids the analytical integration. More generally, for any sortable function $g$,\n",
"This approach is called <font color='orange'>Monte Carlo integration</font> and avoids the analytical integration. More generally, for a function $g$, we get\n",
"\n",
"$$\n",
"\\hat{\\mathbb{E}} (g(\\theta |x)) = \\frac{1}{M} \\sum_{m=1}^M g(\\theta^{(m)}), \\quad \\theta^{(m)} \\sim p(\\theta|x).\n",
"$$"
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