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@jemoka / Jemoka Knowledge Base / wiki/concepts/probabilistic_programming.md
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--- title: "probabilistic programming" type: concept related: [Baysian Parameter Learning, Conjugate Prior] source: https://www.jemoka.com/posts/kbhprobabilistic_programming/ confidence: high status: active --- Remember Bayes Rule in Baysian Parameter Learning: \begin{equation} P\qty(\theta | D) = \frac{P\qty(D | \theta) p \qty(\theta)}{\int_{\theta}P\qty(D | \theta) p \qty(\theta) \dd{\theta}} \end{equation} we can’t actually easily compute the bottom without taking an analytic integral; instead we can sample from it. If you want analytical form, you should hope that your likelihood function is a conjugate prior which allows us to analytically update prirors.