Lecture 12 - Analytical Examples of Bayesian Inference

Objectives

• Explain the mathematical formalism of Bayesian parameter estimation.

• Use Bayesian inference to estimate the parameter of a Bernoulli distribution from observations.

• Use credible intervals to summarize the posterior probability density over a parameter of interest.

• Pose a decision-making problem for selecting a single parameter.

• Explain the concept of posterior predictive checking to assess the quality of a model (replicated data, Bayesian p-values).