Joint Bayesian Treatment of Poisson and Gaussian Experiments in a Chi-squared Statistic

TL;DR

This paper introduces a Bayesian method to convert Poisson distributions into chi-squared form, enabling combined analysis of Poisson and Gaussian data within a unified chi-squared framework, demonstrated through neutrino oscillation studies.

Contribution

It presents an analytical approach to unify Poisson and Gaussian experiments using chi-squared distributions in a Bayesian context, facilitating combined statistical analysis.

Findings

Unified chi-squared treatment for Poisson and Gaussian data

Application to neutrino oscillation experiments

Enhanced analysis flexibility with combined data types

Abstract

Bayesian Poisson probability distributions for the average n can be analytically converted into equivalent chi-squared distributions. These can then be combined with other Gaussian or Bayesian Poisson distributions to make a total chi-squared distribution. This allows the usual treatment of chi-squared contours but now with both Poisson and Gaussian statistics experiments. This is illustrated with the case of neutrino oscillations.