The numerical reconcilability of Bayesian measure and p-value in interval hypotheses is not possible in general

Parisa Zolfaghari, Rahim Chinipardaz and Jafar Esmaily

Communications in Statistics - Theory and Methods, 2023, vol. 52, issue 4, 1178-1189

Abstract: The interval null hypothesis is considered against the two-sided hypothesis. It was shown that p-value in interval null hypothesis can be numerically approximated by p-value of point null when interval converges to a single point of hypothesis. However, it is not true for Bayes factor or posterior probability. When the null hypothesis is substituted to interval one, p-value may be in the range of the posterior probability. In this case, there are a substantial differences between null point and interval null hypothesis in Bayesian measures. The results are shown in more detail in exponential distribution. But can be generalized to gamma distribution.

Date: 2023
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DOI: 10.1080/03610926.2021.1924785

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