A Bayesian Approach To Histogram Comparison

TL;DR

This paper presents a Bayesian method for comparing histograms, including those with importance weights, to determine if they originate from the same distribution, addressing limitations of previous approaches.

Contribution

It introduces a Bayesian model comparison framework for histogram comparison, extending it to handle importance weights common in Monte Carlo simulations.

Findings

Effective in comparing histograms with importance weights

Applicable to both single and multiple distribution hypotheses

Provides a probabilistic measure of histogram consistency

Abstract

Determining if two histograms are consistent, whether they have been drawn from the same underlying distribution or not, is a common problem in physics. Existing approaches are not only limited in power but also inapplicable to histograms filled with importance weights, a common feature of Monte Carlo simulations. From a Bayesian perspective, the comparison between a single underlying distribution and two underlying distributions is readily solved within the context of model comparison. I introduce an implementation of Bayesian model comparison to the problem, including the extension to importance sampling.