Bayesian Block Histogramming for High Energy Physics

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.