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

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.

Comments: 26 pages, with RevTeX. The replacement has added the application to neutrino oscillation experiments. It also includes a more general derivation. For the case with background, it includes a study of the normalization