Quantitative comparisons between finitary posterior distributions and Bayesian posterior distributions

TL;DR

This paper compares finite-horizon Bayesian posterior distributions with traditional infinite-exchangeability-based posteriors to address the gap between theoretical models and practical, empirical applications.

Contribution

It provides a quantitative analysis bridging finitary and Bayesian posterior distributions, enhancing understanding of their differences in statistical inference.

Findings

Finitary posteriors differ quantitatively from Bayesian posteriors.

The comparison offers insights into the applicability of Bayesian methods in finite settings.

Results facilitate better interpretation of Bayesian posteriors in practical scenarios.

Abstract

The main object of Bayesian statistical inference is the determination of posterior distributions. Sometimes these laws are given for quantities devoid of empirical value. This serious drawback vanishes when one confines oneself to considering a finite horizon framework. However, assuming infinite exchangeability gives rise to fairly tractable {\it a posteriori} quantities, which is very attractive in applications. Hence, with a view to a reconciliation between these two aspects of the Bayesian way of reasoning, in this paper we provide quantitative comparisons between posterior distributions of finitary parameters and posterior distributions of allied parameters appearing in usual statistical models.