John D. Cook • 7/12/2026

Posterior variance

This article examines whether additional data always reduces posterior variance in Bayesian statistics, answering with a nuanced 'no'. It reviews three models: beta-binomial, normal-normal, and Poisson-gamma. For the Poisson-gamma model, posterior variance can increase when events are observed, decreasing between observations. Includes an illustration with simulated Poisson data and a gamma prior.

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#Bayesian Statistics #Posterior Variance #Beta Binomial Model