Comparison of Bayesian Credible Intervals and Frequentist Confidence Intervals

• Activity Number: 263
• Type: Contributed
• Date/Time: Monday, August 10, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Kathy Gray* and Casey Bausell and Brittany Hampton and Allison McConnell and Tony Silveti-Falls
• Companies: California State University at Chico and Oregon State University and California State University at Chico and California State University at Chico and California State University at Chico
• Keywords: Credible intervals ; Bayesian ; Frequentist intervals

Abstract

We compared frequentist confidence intervals with Bayesian credible intervals under a variety of scenarios to determine when Bayesian credible intervals outperform frequentist confidence intervals. We investigated how Bayesian intervals compare to frequentist intervals in terms of interval estimation and we also explored how large a sample must be taken in order to approximate the posterior distribution of a parameter with a normal distribution. This involved comparing the capture rates of the parameter as well as the mean squared error for the different interval estimation methods. Our results indicated that for all scenarios with low or no bias in the prior mean, Bayesian interval estimation produces results with precision greater than or equal to the frequentist method. In addition, the shape of the population distribution had little effect on the performance of the Bayesian credible intervals.