Bayesian tests for composite alternative hypotheses in cross-tabulated data

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• 作者：Daniel Yekutieli
• 关键词：Hypotheses testing ; Simpson’s Paradox ; Composite alternative hypotheses ; Exact tests ; Likelihood ratio tests ; Bayes rules ; Bayes factors ; 62C10 ; 62G10
• 刊名：TEST
• 出版年：2015
• 出版时间：June 2015
• 年：2015
• 卷：24
• 期：2
• 页码：287-301
• 全文大小：560 KB
• 参考文献：Agresti A (2002) Categorical data analysis. Wiley, New Jersey
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  Sun W, Cai TT (2007) Oracle and adaptive compound decision rules for false discovery rate control. J Am Stat Assoc 102:901-12View Article MATH MathSciNet
  
• 作者单位：Daniel Yekutieli (1)
  
  1. Department of Statistics and OR, Tel Aviv University, Tel Aviv, 6997801, Israel
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Statistics
  Statistics
  Statistical Theory and Methods
  Statistics for Business, Economics, Mathematical Finance and Insurance
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1863-8260

文摘

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.