Part XVI — Bayesian Statistics

Inference that treats parameters as random: priors, posteriors, conjugacy, updating, and the model-comparison and prediction machinery built on the posterior.

Topics

Topic	Focus
The Bayesian Framework	Priors, posteriors, and Bayesian point estimates (MAP and LMS)
Prior Distributions	Encoding beliefs before seeing data
Posterior Distributions	The distribution of parameters after seeing data
Conjugate Priors	Prior families that keep posteriors in closed form
Bayesian Updating	Sequential prior-to-posterior updating, worked on a coin's unknown bias
Bayesian Model Comparison	Comparing models by marginal likelihood
Bayesian Prediction	Predictive distributions that average over parameter uncertainty