Decision theoretic Bayesian hypothesis testing with the selection goal

Decision Theoretic Bayesian Hypothesis Testing with the Selection Goal

Consider a probability model P ; ; where = ( 1; 2; :::; k) is a parameter vector of interest, and is some nuisance parameter. The problem of testing null hypothesis H0 : 1 = 2 = ::: = k against selecting one of k alternative hypotheses Hi : i = [k] > [1]; i = 1; 2; :::; k; where [k] = maxf 1; 2; :::; kg and [1] = minf 1; 2; :::; kg; is formulated from a Bayesian decision theoretic point of view...

A Bayesian Decision-Theoretic Approach to Logically-Consistent Hypothesis Testing

This work addresses an important issue regarding the performance of simultaneous test procedures: the construction of multiple tests that at the same time are optimal from a statistical perspective and that also yield logically-consistent results that are easy to communicate to practitioners of statistical methods. For instance, if hypothesis A implies hypothesis B, is it possible to create opt...

Bayesian Fuzzy Hypothesis Testing with Imprecise Prior Distribution

This paper considers the testing of fuzzy hypotheses on the basis of a Bayesian approach. For this, using a notion of prior distribution with interval or fuzzy-valued parameters, we extend a concept of posterior probability of a fuzzy hypothesis. Some of its properties are also put into investigation. The feasibility and effectiveness of the proposed methods are also cla...

Bayesian Hypothesis Testing 1 Running head: BAYESIAN HYPOTHESIS TESTING The Need for Bayesian Hypothesis Testing in Psychological Science

Testing Hypothesis with Single Molecules: Bayesian Approach