Variations on the Expectation due to Changes in the Probability Measure

TL;DR

This paper derives closed-form formulas for how expectations change when the underlying probability measure varies, revealing links with Gibbs measures, mutual information, and lautum information.

Contribution

It introduces new closed-form expressions for expectation variations under measure changes, connecting them to key concepts in information theory.

Findings

Closed-form expressions for expectation variation

Connections with Gibbs measures and information metrics

Insights into the relationship between measure changes and information measures

Abstract

In this paper, closed-form expressions are presented for the variation of the expectation of a given function due to changes in the probability measure used for the expectation. They unveil interesting connections with Gibbs probability measures, mutual information, and lautum information.