Bayesian tests for composite alternative hypotheses in cross-tabulated data

• Daniel Yekutieli ^[1]
  1. [1] Tel Aviv University

     Tel Aviv University

     Israel

     
• Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 24, Nº. 2, 2015, págs. 287-301
• Idioma: inglés
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• Resumen

  • We present a methodology for constructing significance tests for “difficult” composite alternative hypotheses that have no natural test statistic. We apply our methodology to construct exact tests for cross-tabulated data, and our motivating example is constructing a test for discovering Simpson’s Paradox. Our tests are Bayesian extensions of the likelihood ratio test; they are optimal with respect to the prior distribution and are also closely related to Bayes factors and Bayesian FDR controlling testing procedures.