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Bayesian model selection using test statistics

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  • Jianhua Hu
  • Valen E. Johnson

Abstract

Summary. Existing Bayesian model selection procedures require the specification of prior distributions on the parameters appearing in every model in the selection set. In practice, this requirement limits the application of Bayesian model selection methodology. To overcome this limitation, we propose a new approach towards Bayesian model selection that uses classical test statistics to compute Bayes factors between possible models. In several test cases, our approach produces results that are similar to previously proposed Bayesian model selection and model averaging techniques in which prior distributions were carefully chosen. In addition to eliminating the requirement to specify complicated prior distributions, this method offers important computational and algorithmic advantages over existing simulation‐based methods. Because it is easy to evaluate the operating characteristics of this procedure for a given sample size and specified number of covariates, our method facilitates the selection of hyperparameter values through prior‐predictive simulation.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jorssb:v:71:y:2009:i:1:p:143-158
    DOI: 10.1111/j.1467-9868.2008.00678.x
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    References listed on IDEAS

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    1. 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.
    2. Taniguchi, Masanobu, 1991. "Third-order asymptomic properties of a class of test statistics under a local alternative," Journal of Multivariate Analysis, Elsevier, vol. 37(2), pages 223-238, May.
    3. 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.
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    Cited by:

    1. Kirgios, Erika L. & Chang, Edward H. & Milkman, Katherine L., 2020. "Going it alone: Competition increases the attractiveness of minority status," Organizational Behavior and Human Decision Processes, Elsevier, vol. 161(C), pages 20-33.
    2. Heyard, Rachel & Held, Leonhard, 2019. "The quantile probability model," Computational Statistics & Data Analysis, Elsevier, vol. 132(C), pages 84-99.
    3. Yu, Chi Wai & Clarke, Bertrand, 2010. "Asymptotics of Bayesian median loss estimation," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 1950-1958, October.
    4. 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.
    5. 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.

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