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

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  • Parisa Zolfaghari
  • Rahim Chinipardaz
  • Jafar Esmaily

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.

Suggested Citation

  • Parisa Zolfaghari & Rahim Chinipardaz & Jafar Esmaily, 2023. "The numerical reconcilability of Bayesian measure and p-value in interval hypotheses is not possible in general," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 52(4), pages 1178-1189, February.
    • Handle: RePEc:taf:lstaxx:v:52:y:2023:i:4:p:1178-1189
    DOI: 10.1080/03610926.2021.1924785
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