Update of prior probabilities by minimal divergence

TL;DR

This paper explores methods for updating empirical probability distributions using minimal divergence measures, specifically Hellinger distance and quadratic Bregman divergence, including updates with conditional probabilities.

Contribution

It introduces a comparative analysis of two divergence-based methods for updating probabilities and extends the framework to incorporate conditional probability information.

Findings

Hellinger and Bregman divergence methods yield different updated distributions.

Inclusion of conditional probabilities enhances the update process.

The paper provides theoretical insights into divergence-based probability updates.

Abstract

The present paper investigates the update of an empirical probability distribution with the results of a new set of observations. The optimal update is obtained by minimizing either the Hellinger distance or the quadratic Bregman divergence. The results obtained by the two methods differ. Updates with information about conditional probabilities are considered as well.