- Bayesian learning uses Bayes' rule to update one's beliefs about a parameter θ after observing data y. The prior distribution describes beliefs about θ before seeing y, while the posterior distribution describes beliefs after seeing y. - For a binomial example of coin flipping, the posterior distribution is a beta distribution that is proportional to the prior beta distribution multiplied by the binomial likelihood. - A prior distribution is conjugate if the posterior has the same distributional form as the prior. Many common distributions like binomial and normal have conjugate priors. - The posterior represents a compromise between the prior and likelihood, with the posterior mean a weighted average of the prior and data means, and the posterior precision being the sum of the prior and data precisions