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Bayes factors based on test statistics

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  • Valen E. Johnson

Abstract

Summary. Traditionally, the use of Bayes factors has required the specification of proper prior distributions on model parameters that are implicit to both null and alternative hypotheses. I describe an approach to defining Bayes factors based on modelling test statistics. Because the distributions of test statistics do not depend on unknown model parameters, this approach eliminates much of the subjectivity that is normally associated with the definition of Bayes factors. For standard test statistics, including the χ2‐, F‐, t‐ and z‐statistics, the values of Bayes factors that result from this approach have simple, closed form expressions.

Suggested Citation

  • Valen E. Johnson, 2005. "Bayes factors based on test statistics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 689-701, November.
    • Handle: RePEc:bla:jorssb:v:67:y:2005:i:5:p:689-701
    DOI: 10.1111/j.1467-9868.2005.00521.x
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    Cited by:

    1. van Doorn, Johnny & Ly, Alexander & Marsman, Maarten & Wagenmakers, Eric-Jan, 2019. "Bayesian estimation of Kendall’s τ using a latent normal approach," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 268-272.
    2. Magris Martin & Iosifidis Alexandros, 2021. "Approximate Bayes factors for unit root testing," Papers 2102.10048, arXiv.org, revised Feb 2021.
    3. 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.
    4. Mariusz Czekala & Zbigniew Kurylek, 2021. "Inversions Distribution and Testing Correlation Changes for Rates of Return," European Research Studies Journal, European Research Studies Journal, vol. 0(3B), pages 633-650.
    5. 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.
    6. 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.
    7. Wang, Linglu & Li, Qizhai & Li, Zhaohai & Zheng, Gang, 2011. "Bayes factors in the presence of population stratification," Statistics & Probability Letters, Elsevier, vol. 81(7), pages 836-841, July.
    8. 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.
    9. Michael J. Daniels & Arkendu S. Chatterjee & Chenguang Wang, 2012. "Bayesian Model Selection for Incomplete Data Using the Posterior Predictive Distribution," Biometrics, The International Biometric Society, vol. 68(4), pages 1055-1063, December.
    10. Zhang, Jingsi & Jiang, Wenxin & Shao, Xiaofeng, 2013. "Bayesian model selection based on parameter estimates from subsamples," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 979-986.
    11. Mary Meyer & Amber Hackstadt & Jennifer Hoeting, 2011. "Bayesian estimation and inference for generalised partial linear models using shape-restricted splines," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(4), pages 867-884.

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