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Coherence of the posterior predictive p-value based on the posterior odds

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  • Horra Navarro, J. de la
  • Rodríguez Bernal, M. T.

Abstract

^aIt is well-known that classical p-values sometimes behave incoherently for testing hypotheses in the sense that, when $\Theta_{0} \subset \Theta_{0}{'}$, the support given to $\Theta_{0}$ is greater than or equal to the support given to $\Theta_{0}^{'}$ . This problem is also found for posterior predictive p-values (a Bayesian-motivated alternative to classical p-values). In this paper, it is proved that, under some conditions, the posterior predictive p-value based on the posterior odds is coherent, showing that the choice of a suitable discrepancy variable is crucial.

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  • Horra Navarro, J. de la & Rodríguez Bernal, M. T., 2001. "Coherence of the posterior predictive p-value based on the posterior odds," DES - Working Papers. Statistics and Econometrics. WS ws012516, Universidad Carlos III de Madrid. Departamento de Estadística.
  • Handle: RePEc:cte:wsrepe:ws012516
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    1. Julián Horra & María Rodríguez-Bernal, 1999. "The posterior predictive p-value for the problem of goodness of fit," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 8(1), pages 117-128, June.
    2. Thompson, Peter, 1997. "Bayes p-values," Statistics & Probability Letters, Elsevier, vol. 31(4), pages 267-274, February.
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    1. Julián Horra & M. Rodriguez-Bernal, 2001. "Posterior predictive p-values: what they are and what they are not," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 10(1), pages 75-86, June.

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