Bayesian Hypothesis Testing: a Reference Approach

Bayesian Hypothesis Testing: A Reference Approach

For any probability model M ≡ {p(x |θ,ω),θ ∈ Θ,ω ∈ Ω} assumed to describe the probabilistic behaviour of data x ∈ X, it is argued that testing whether or not the available data are compatible with the hypothesis H0 ≡ {θ = θ0} is best considered as a formal decision problem on whether to use (a0), or not to use (a1), the simpler probability model (or null model) M0 ≡ {p(x |θ0,ω),ω ∈ Ω}, where th...

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...

Testing Hypothesis with Single Molecules: Bayesian Approach

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