Bayesian Block Histogramming for High Energy Physics

TL;DR

This paper adapts the Bayesian Block algorithm from astronomy to high energy physics, improving histogram binning for better data visualization and non-parametric background estimation, aiding in data analysis and new physics searches.

Contribution

It introduces Bayesian Block histogramming to high energy physics, providing an adaptive, non-parametric density estimation method that enhances data presentation and hypothesis testing.

Findings

Improved histogram binning visually enhances data interpretation.

Non-parametric background estimation avoids arbitrary analytical functions.

Demonstrated effectiveness in identifying peaks and tails in data.

Abstract

The Bayesian Block algorithm, originally developed for applications in astronomy, can be used to improve the binning of histograms in high energy physics. The visual improvement can be dramatic, as shown here with two simple examples. More importantly, this algorithm and the histogram is produces is a non-parametric density estimate, providing a description of background distributions that does not suffer from the arbitrariness of ad hoc analytical functions. The statistical power of an hypothesis test based on Bayesian Blocks is nearly as good as that obtained by fitting analytical functions. Two examples are provided: a narrow peak on a smoothly-falling background, and an excess in the tail of a background that falls rapidly over several orders of magnitude. These examples show the usefulness of the binning provided by the Bayesian Blocks algorithm both for presentation of data and when searching for new physics.