C2. Conjugacy
What is a conjugate prior family? Give one prior–sampling-model example.
Worked answer (click to show)
Definitions/notation. A prior family is conjugate for a sampling model if Bayesian updating keeps the posterior in that family, with updated hyperparameters. For example, a \operatorname{Beta}(a,b) prior for a binomial success probability yields \operatorname{Beta}(a+x,b+n-x) after x successes in n trials, where a,b>0.