Logical coherence in Bayesian simultaneous three-way hypothesis tests
Statistics Theory
2022-04-05 v1 Statistics Theory
Abstract
This paper studies whether Bayesian simultaneous three-way hypothesis tests can be logically coherent. Two types of results are obtained. First, under the standard error-wise constant loss, only for a limited set of models can a Bayes simultaneous test be logically coherent. Second, if more general loss functions are used, then it is possible to obtain Bayes simultaneous tests that are always logically coherent. An explicit example of such a loss function is provided.
Cite
@article{arxiv.2204.01495,
title = {Logical coherence in Bayesian simultaneous three-way hypothesis tests},
author = {Bernardo F. Reimann and Rafael Izbicki and Julio M. Stern and Rafael B. Stern and Luis G. Esteves},
journal= {arXiv preprint arXiv:2204.01495},
year = {2022}
}
Comments
19 pages, 1 figure