2026/07/31 by Antonio R. Linero
Mathematics · #math.ST #stat.TH
arxiv created 2026/07/31 · arxiv updated 2026/08/03
I present a very simple example in which a full-support prior over distribution functions has an inconsistent posterior, which I believe has instructive value. The example is Yi \stackreliid∼ P0 under the Bayesian hierarchical model [Yi | P] \stackreliid∼ P and P ∼ ∫ DP(α, H) πα(α) dα when πα(⋅) has exponential (or heavier) tails, where DP(α, H) denotes a Dirichlet process with concentration parameter α and mean H(⋅); on the other hand, consistency is obtained under a light-tailed prior. This unifies and generalizes a consistency result of Freedman and Diaconis (1983) with an inconsistency result described by Ferguson et al. (1992).