On uniform continuity of posterior distributions

TL;DR

This paper establishes conditions under which posterior distributions are strongly continuous with respect to data in dominated models, with applications to exponential models, enhancing understanding of Bayesian stability.

Contribution

It provides new conditions for strong posterior continuity in dominated models, especially applied to exponential families, advancing theoretical understanding of Bayesian robustness.

Findings

Posterior distributions exhibit strong continuity under specified conditions.

Applications demonstrate the relevance to exponential models.

Results improve theoretical insights into Bayesian stability.

Abstract

In the setting of dominated statistical models, we provide conditions yielding strong continuity of the posterior distribution with respect to the observed data. We show some applications, with special focus on exponential models.