Calculate the posterior probability given a prior distribution and observed evidence.
The posterior probability updates our belief in a hypothesis after observing evidence. It uses the total probability rule to compute P(E) from both the true and false hypotheses, then applies Bayes' theorem. This is the fundamental operation in Bayesian inference and sequential updating.
Posterior via Bayes
P(H|E) = P(E|H)*P(H) / [P(E|H)*P(H) + P(E|~H)*P(~H)]
Yes — this is sequential Bayesian updating. After observing new evidence, today's posterior becomes tomorrow's prior, allowing beliefs to be continuously refined as data arrives.
Bayesian NNs maintain a posterior distribution over weights rather than point estimates, enabling uncertainty quantification. The posterior is updated via approximate methods like variational inference.