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Bayesian hypotheses testing using posterior density ratios

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  • Basu, Sanjib

Abstract

The posterior density ratio sup[theta][epsilon]Ho [pi]([theta]data)/sup[theta][epsilon]H1 [pi]([theta]data) is proposed as a new criterion for Bayesian hypothesis testing. The performances of the posterior density ratio and the posterior probability of Ho are compared in point null hypothesis, precise hypothesis and one sided hypothesis tests. It is found that the likelihood ratio and the lower bound of the posterior density ratio over a scale mixture class of priors match in point null hypothesis testing. They, however, do not match in one sided testing.

Suggested Citation

  • Basu, Sanjib, 1996. "Bayesian hypotheses testing using posterior density ratios," Statistics & Probability Letters, Elsevier, vol. 30(1), pages 79-86, September.
    • Handle: RePEc:eee:stapro:v:30:y:1996:i:1:p:79-86
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    References listed on IDEAS

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    1. James Berger & Elías Moreno & Luis Pericchi & M. Bayarri & José Bernardo & Juan Cano & Julián Horra & Jacinto Martín & David Ríos-Insúa & Bruno Betrò & A. Dasgupta & Paul Gustafson & Larry Wasserman &, 1994. "An overview of robust Bayesian analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 3(1), pages 5-124, June.
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