In the context of probability theory, the terms prior, evidence, and posterior refer to components in Bayes’ theorem: $ p(x \mid y) = \frac{p(x \cap y)}{p(y)} = \frac{p(y \mid x) \, p(x)}{p(y)} $ ## Breakdown 1. **Posterior $p(x \mid y)$**: This is the probability of $x$ given $y$. It’s called the posterior because it represents the updated belief about $x$ after observing $y$. 2. **Likelihood $p(y \mid x)$**: This is the probability of observing $y$ given that $x$ is true. It reflects how likely it is to observe $y$ under the assumption of $x$ occurring. 3. **Prior $p(x)$**: This is the initial belief or probability about $x$ before any evidence $y$ is taken into account. 4. **Evidence $p(y)$**: This is the probability of observing $y$ under all possible scenarios, which serves as a normalizing factor to ensure that the posterior probability is properly scaled.