Bayesian (mean) most powerful tests

Bayesian (mean) most powerful tests

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Article ID: iaor2017841
Volume: 59
Issue: 1
Start Page Number: 43
End Page Number: 56
Publication Date: Mar 2017
Journal: Australian & New Zealand Journal of Statistics
Authors:
Keywords: experiment, statistics: experiment, testing
Abstract:

A fundamental theorem in hypothesis testing is the Neyman‐Pearson (N‐P) lemma, which creates the most powerful test of simple hypotheses. In this article, we establish Bayesian framework of hypothesis testing, and extend the Neyman‐Pearson lemma to create the Bayesian most powerful test of general hypotheses, thus providing optimality theory to determine thresholds of Bayes factors. Unlike conventional Bayes tests, the proposed Bayesian test is able to control the type I error.

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