Chi-square Intervals for a Poisson Parameter - Bayes, Classical and Structural

TL;DR

This paper explores various chi-square based confidence intervals for estimating a Poisson parameter, comparing classical, Bayesian, and structural methods, and evaluates their coverage probabilities for validation purposes.

Contribution

It introduces and compares multiple chi-square intervals for Poisson parameters, including Bayesian and structural approaches, and assesses their coverage probabilities.

Findings

Coverage probabilities vary across different intervals.

Bayesian and structural intervals can be validated using coverage probabilities.

Alternative chi-square intervals provide options beyond standard methods.

Abstract

The 'standard' confidence interval for a Poisson parameter is only one of a number of estimation intervals based on the chi-square distribution that may be used in the estimation of the mean or mean rate for a Poisson model. Other chi-square intervals are available for experimenters using Bayesian or structural inference methods. Exploring these intervals also leads to other alternate approximate chi-square intervals. Although coverage probability may not always be of interest for Bayesian or structural intervals, coverage probabilities are useful for validating 'objective' priors. Coverage probabilities are explored for all of the intervals considered.