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Objective Bayesian testing for the linear combinations of normal means

Author

Listed:
  • Woo Dong Lee

    (Daegu Haany University)

  • Sang Gil Kang

    (Sangji University)

  • Yongku Kim

    (Kyungpook National University)

Abstract

This study considers objective Bayesian testing for the linear combinations of the means of several normal populations. We propose solutions based on a Bayesian model selection procedure to this problem in which no subjective input is considered. We first construct suitable priors to test the linear combinations of means based on measuring the divergence between competing models (so-called divergence-based priors). Next, we derive the intrinsic priors for which the Bayes factors and model selection probabilities are well defined. Finally, the behavior of the Bayes factors based on the DB priors, intrinsic priors, and classical test are compared in a simulation study and an example.

Suggested Citation

  • Woo Dong Lee & Sang Gil Kang & Yongku Kim, 2019. "Objective Bayesian testing for the linear combinations of normal means," Statistical Papers, Springer, vol. 60(1), pages 147-172, February.
    • Handle: RePEc:spr:stpapr:v:60:y:2019:i:1:d:10.1007_s00362-016-0831-2
    DOI: 10.1007/s00362-016-0831-2
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    References listed on IDEAS

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    1. M. J. Bayarri & G. García‐Donato, 2008. "Generalization of Jeffreys divergence‐based priors for Bayesian hypothesis testing," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(5), pages 981-1003, November.
    2. Dal Kim & Sang Kang & Woo Lee, 2006. "Noninformative priors for linear combinations of the normal means," Statistical Papers, Springer, vol. 47(2), pages 249-262, March.
    3. José M. Bernardo & Raúl Rueda, 2002. "Bayesian Hypothesis Testing: a Reference Approach," International Statistical Review, International Statistical Institute, vol. 70(3), pages 351-372, December.
    4. Fulvio De Santis & Fulvio Spezzaferri, 1999. "Methods for Default and Robust Bayesian Model Comparison: the Fractional Bayes Factor Approach," International Statistical Review, International Statistical Institute, vol. 67(3), pages 267-286, December.
    Full references (including those not matched with items on IDEAS)

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