Maximum entropy method: sampling bias

TL;DR

This paper examines sampling bias in the maximum entropy method when using finite data sets, proposing a more flexible approach that avoids forcing expectation values to match experimental averages, with illustrative examples.

Contribution

It introduces a general formulation for addressing sampling bias in maximum entropy methods without strictly equating expectation values to sample averages.

Findings

Identifies issues with sampling bias in finite data maximum entropy applications

Proposes a flexible approach to mitigate sampling bias

Provides illustrative examples demonstrating the concepts

Abstract

Maximum entropy method is a constructive criterion for setting up a probability distribution maximally non-committal to missing information on the basis of partial knowledge, usually stated as constrains on expectation values of some functions. In connection with experiments sample average of those functions are used as surrogate of the expectation values. We address sampling bias in maximum entropy approaches with finite data sets without forcedly equating expectation values to corresponding experimental average values. Though we rise the approach in a general formulation, the equations are unfortunately complicated. We bring simple case examples, hopping clear but sufficient illustration of the concepts.