Frequentist vs. Bayesian Confidence Intervals

Two-sided confidence intervals for the parameter p of a Binomial distribution under a prescribed confidence level are an elementary tool of statistical data analysis. The two basic quality characteristics of a confidence interval are whether the actual coverage probability exceeds a prescribed level and its length. In this seminar I present a scheme to obtain minimum volume confidence intervals for a probability p that maintain a confidence level γ and allow exploiting prior information on the parameter p. The approach is a frequentist approach and prior information is expressed by a beta distribution. I compare the frequentist scheme with the Bayesian HPD credibility intervals by imposing a beta prior and analyze the performance of the intervals in terms of coverage probability and length. Useful applications in the case when prior information on the probability p is available, e. g. when p is known to be very small like in the context of audit sampling, credit risk or quality control.