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Bayesian and frequentist evidence in one-sided hypothesis testing

Author

Listed:
  • Elías Moreno

    (University of Granada)

  • Carmen Martínez

    (University of Granada)

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.

Suggested Citation

  • Elías Moreno & Carmen Martínez, 2022. "Bayesian and frequentist evidence in one-sided hypothesis testing," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(1), pages 278-297, March.
    • Handle: RePEc:spr:testjl:v:31:y:2022:i:1:d:10.1007_s11749-021-00778-8
    DOI: 10.1007/s11749-021-00778-8
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    References listed on IDEAS

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    1. Mulder, Joris, 2014. "Prior adjusted default Bayes factors for testing (in)equality constrained hypotheses," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 448-463.
    2. F. Javier Girón & M. Lina Martínez & Elías Moreno & Francisco Torres, 2006. "Objective Testing Procedures in Linear Models: Calibration of the p‐values," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(4), pages 765-784, December.
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