Posterior Probabilities: Dominance and Optimism

TL;DR

This paper explores the properties of Bayesian posterior probabilities, demonstrating that the true state's posterior is stochastically dominated and introducing the concept of 'optimism' in posterior assessments.

Contribution

It generalizes the dominance property of posterior probabilities to include notions of optimism, providing new theoretical insights into Bayesian inference.

Findings

Posterior probability of the true state is stochastically dominated.

Introduction of the concept of 'optimism' in posterior probabilities.

Generalization of dominance properties to broader notions of belief.

Abstract

The Bayesian posterior probability of the true state is stochastically dominated by that same posterior under the probability law of the true state. This generalizes to notions of "optimism" about posterior probabilities.