EVALUATING THE ACCURACY OF CLASSICAL AND BAYESIAN CONFIDENCE INTERVALS FOR THE POISSON MEAN

Abstract

This research aims to evaluate and compare classical (frequentist) confidence intervals and Bayesian confidence intervals in estimating the mean of the Poisson distribution (λ).

The study relied on a systematic computer simulation approach to compare the main classical methods (such as Garwood, modified Wald, Begaud) and Bayesian methods (such as Jeffreys and HPD). The simulations were conducted by generating 10,000 Poisson samples for various λ levels (0.1–20) and sample sizes (n) (5–100).

Custom Python algorithms were used: SciPy to calculate inverse distributions, NumPy for statistical simulation, and Matplotlib to visualize the results.

The evaluation criteria were applied: actual coverage (% coverage), expected interval length (E(L)), and non-coverage equilibrium.

And The important results that research reached is following: Bayesian superiority in small samples: Bayesian-Jeffreys intervals achieved coverage closer to the 95% confidence level when n<30 (coverage: 92–94% versus 85–90% for classical methods).

Narrow Bayesian intervals: Bayesian HPD intervals were 15–30% shorter than classical methods when λ<5.

Performance of classical methods: Garwood's (exact) method demonstrated overconservatism (coverage up to 98%), increasing the interval length by 40% when n=10.