An Objective Bayesian Approach to Multistage Hypothesis Testing

Abstract

A new Bayesian approach to multistage hypothesis testing is considered. Prior is derived using Jeffreys’ criterion on likelihood associated with the design information. We show that the prior for sequential Bernoulli design asymptotically converges toward the Jeffreys prior in Pascal sampling model. A general rule is given for determining the design-corrected version of default priors when Jeffreys’ criterion results in improper distribution. Based on the principle of design impartiality, the Bayes factor as posterior-based evidential measure can be generalized to multistage testing, so that the decision boundaries reflect equal evidence for hypotheses over stages. Effect of prior correction on design parameters and on Bayesian inference upon test termination is studied. The approach is applied to a three-stage binomial design. Last, the use of the prior as the default objective choice in multistage hypothesis testing is discussed.

Keywords:

• Bayes factor
• Frequentist characteristics
• Jeffreys’ criterion
• Likelihood principle
• Objective prior

Subject Classifications:

• 62F03
• 62F15
• 62L05

ACKNOWLEDGMENTS

The authors are indebted to the anonymous referee, the Associate Editor, and the Editor for their helpful comments.

Notes

Acc =accept; ND =no decision; and Rej =reject.

Recommended by Adam Martinsek