1 - Introduction
An inference problem requires statements about the value of an unobserved (latent) variable x based on observations y which are related to x, but may not be sufficient to fully determine x. This requires a notion of uncertainty.
We can define the following rules because \(p(E) = 1\) for any event \(E\).
- Sum rule: \(p(E) = p(E|A) + p(E|\neg A)\)
- Product rule: \(p(E, A) = p(E|A)p(A) = p(A|E)p(E)\)
- Bayes’ theorem: \(p(E|A) = \frac{p(A|E)p(E)}{p(A)}\)