Bayesian tests for composite alternative hypotheses in cross-tabulated data

Daniel Yekutieli*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)287-301
Number of pages15
JournalTest
Volume24
Issue number2
DOIs
StatePublished - 17 Oct 2015

Keywords

  • Bayes factors
  • Bayes rules
  • Composite alternative hypotheses
  • Exact tests
  • Hypotheses testing
  • Likelihood ratio tests
  • Simpson’s Paradox

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