Bayesian and frequentist evidence in one-sided hypothesis testing

Elías Moreno () and Carmen Martínez ()
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Elías Moreno: University of Granada
Carmen Martínez: University of Granada

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2022, vol. 31, issue 1, No 12, 278-297

Abstract: Abstract In one-sided testing, Bayesians and frequentists differ on whether or not there is discrepancy between the inference based on the posterior model probability and that based on the p value. We add some arguments to this debate analyzing the discrepancy for moderate and large sample sizes. For small and moderate samples sizes, the discrepancy is measured by the probability of disagreement. Examples of the discrepancy on some basic sampling models indicate the somewhat unexpected result that the probability of disagreement is larger when sampling from models in the alternative hypothesis that are not located at the boundary of the hypotheses. For large sample sizes, we prove that the Bayesian one-sided testing is, under mild conditions, consistent, a property that is not shared by the frequentist procedure. Further, the rate of convergence is $$O(e^{nA})$$ O ( e nA ) , where A is a constant that depends on the model from which we are sampling. Consistency is also proved for an extension to multiple hypotheses.

Keywords: Bayesian one-sided test; Consistency; Decision rule; Intrinsic priors; p Values; Reference priors; 62F15; 62F03 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s11749-021-00778-8

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