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Properties of Bayes Factors Based on Test Statistics

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  • VALEN E. JOHNSON

Abstract

. This article examines the consistency, interpretation and application of Bayes factors constructed from standard test statistics. Primary conclusions are that Bayes factors based on multinomial and normal test statistics are consistent for suitable choices of the hyperparameters used to specify alternative hypotheses, and that such constructions can be extended to obtain consistent Bayes factors based on likelihood ratio statistics. A connection between Bayes factors based on likelihood ratio statistics and the Bayesian information criterion is exposed, as is a connection between Bayes factors based on F statistics and parametric Bayes factors based on normal‐inverse gamma models. Similarly, Bayes factors based on chi‐squared statistics for multinomial data are shown to provide accurate approximations to Bayes factors based on multinomial/Dirichlet models. An illustration of how the simple form of these Bayes factors can be exploited to generate easily interpretable summaries of the experimental ‘weight of evidence’ is provided.

Suggested Citation

  • Valen E. Johnson, 2008. "Properties of Bayes Factors Based on Test Statistics," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(2), pages 354-368, June.
    • Handle: RePEc:bla:scjsta:v:35:y:2008:i:2:p:354-368
    DOI: 10.1111/j.1467-9469.2007.00576.x
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    Cited by:

    1. Yuan Min & Pan Xiaoqing & Yang Yaning, 2015. "Bayes factors based on robust TDT-type tests for family trio design," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 14(3), pages 253-264, June.
    2. Heyard, Rachel & Held, Leonhard, 2019. "The quantile probability model," Computational Statistics & Data Analysis, Elsevier, vol. 132(C), pages 84-99.
    3. Jianhua Hu & Valen E. Johnson, 2009. "Bayesian model selection using test statistics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(1), pages 143-158, January.
    4. Xiaoquan Wen, 2017. "Robust Bayesian FDR Control Using Bayes Factors, with Applications to Multi-tissue eQTL Discovery," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 9(1), pages 28-49, June.
    5. Xiaoquan Wen, 2014. "Bayesian model selection in complex linear systems, as illustrated in genetic association studies," Biometrics, The International Biometric Society, vol. 70(1), pages 73-83, March.

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