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@jemoka / Jemoka Knowledge Base / wiki/concepts/bayes_theorem.md
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--- title: "Bayes Theorem" type: concept source: https://www.jemoka.com/posts/kbhbayes_theorem/ confidence: high status: active --- \begin{align} p(x\mid y) = \frac{p(y \mid x) p(x)}{p(y)} \end{align} this is a direct result of the probability chain rule. Typically, we name \(p(y|x)\) the “likelihood”, \(p(x)\) the “prior”. Better normalization What if you don’t fully know \(p(y)\), say it was parameterized over \(x\)? \begin{align} p(x|y) &= \frac{p(y|x) \cdot p(x)}{p(y)} \\ &= \frac{p(y|x) \cdot p(x)}{\sum_{X_{i}} p(y|X_{i})} \end{align} just apply law of total probability! taad