Bayes

We can ignore terms that are constant with regard to the distribution we are computing. For instance, for a fixed x*,

but we can ignore p(x) since we are interested in a distribution with respect to z. To get this distribution, we can evaluate p(x | z) p(z) at all z and ensure it integrates to 1 by rescaling it by C ignoring the need for p(x*) term (which is 1/C).

TO DO: Find notes about ‘evidence’ in Bayes

Posterior = Likelihood (of data) * Prior (probability of Hypothesis) / Probability of Data

Posterior = Likelihood * Prior / Evidence

Likelihood = likelihood of data give hypothesis, multiplies posterior probability

Hypothesis = Prior probability of Hypothesis, multiplies the posterior probability of hypothesis

Data = probability of data, the lower this is, the higher the posterior probability of hypothesis

Likeli

Last Reviewed: 1/25/25