On the relation between frequentist and Bayesian approaches for the case of Poisson statistics

2012/06/18 by S. I. Bitioukov, Sergey Bitioukov, Bitioukov, Sergey +2
Earth and Planetary Sciences · Engineering · Mathematics · Physics and Astronomy · #Data Analysis #FOS: Computer and information sciences #FOS: Physical sciences #Methodology (stat.ME) #Reservoir Engineering and Simulation Methods #Seismic Imaging and Inversion Techniques #Statistics and Probability (physics.data-an) #physics.data-an #stat.ME

paper · pdf · doi:10.48550/arxiv.1206.3991

9 pages

arxiv created 2012/06/18 · openalex publication_date 2012/06/18 · arxiv updated 2012/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We propose modified frequentist definition for the determination of confidence intervals for the case of Poisson statistics. Namely, we require that 1-β' ≥ ∑_n=o^n_obs+k P(n|λ) ≥ α'. We show that this definition is equivalent to the Bayesian method with prior π(λ) ∼ λ^k. We also propose modified frequentist definition for the case of nonzero background.

Related

• Enhancing the physical significance of Frequentist confidence intervals
• The relation between frequentist confidence intervals and Bayesian credible intervals
• Confidence intervals for the parameter of Poisson distribution in presence of background
• Confidence Intervals for Poisson Distribution Parameter
• Expected Coverage of Bayesian Confidence Intervals for the Mean of a Poisson Statistic in Measurements with Background