An Objective Bayesian Approach to Multistage Hypothesis Testing

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 m...

Full description

Saved in:
Bibliographic Details
Published in:Sequential analysis 2010-01, Vol.29 (1), p.88-101
Main Authors: Bunouf, Pierre, Lecoutre, Bruno
Format: Article
Language:English
Subjects:
Asymptotic methods
Bayes factor
Bayesian analysis
Binomial distribution
Frequentist characteristics
Hypothesis testing
Jeffreys' criterion
Likelihood principle
Mathematics
Methodology
Objective prior
Statistics
Statistics Theory
Studies
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0747-4946
1532-4176
DOI:10.1080/07474940903482452