A conjugate prior belongs to a family whose posterior remains in that family after multiplication by the likelihood.
For an exponential family with density proportional to , its natural conjugate prior has density proportional to . Observations update by adding sufficient statistics and update by adding sample size.
Articles by others on the same topic
In Bayesian statistics, a **conjugate prior** is a type of prior probability distribution that, when used in conjunction with a particular likelihood function, results in a posterior distribution that is in the same family as the prior distribution. This property makes the mathematical analysis and computations more tractable.