Reducing multi-dimensional information into a 1-d histogram

TL;DR

This paper introduces two methods for reducing multidimensional data to a single dimension, facilitating analysis while preserving statistical power, with applications in physics where features like mass peaks are relevant.

Contribution

It presents two existing methods adapted for high-energy physics, one incorporating a signal model to improve statistical power at the cost of model dependence.

Findings

Both methods effectively reduce dimensions in physics data.

One method enhances power using a signal model.

The approaches are applicable in areas with distinctive features.

Abstract

We present two methods for reducing multidimensional information to one dimension for ease of understand or analysis while maintaining statistical power. While not new, dimensional reduction is not greatly used in high-energy physics and has applications whenever there is a distinctive feature (for instance, a mass peak) in one variable but when signal purity depends on others; so in practice in most of the areas of physics analysis. While both methods presented here assume knowledge of the background, they differ in the fact that only one of the methods uses a model for the signal, trading some increase in statistical power for this model dependence.