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Exact statistical solutions using the inverse Bayes formulae

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  • Tian, Guo-Liang
  • Tan, Ming

Abstract

This article extends the inverse Bayes formulae (IBF) in the product measurable space (PMS) to the nonproduct measurable space (NPMS) and focuses on their applications in compatibility checking and Bayesian computation. We show that IBF hold only in PMS and derive the modified IBF in NPMS. The potential of using IBF in obtaining exact solution is demonstrated via problems in distribution theory and several Bayesian missing data models.

Suggested Citation

  • Tian, Guo-Liang & Tan, Ming, 2003. "Exact statistical solutions using the inverse Bayes formulae," Statistics & Probability Letters, Elsevier, vol. 62(3), pages 305-315, April.
    • Handle: RePEc:eee:stapro:v:62:y:2003:i:3:p:305-315
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    Cited by:

    1. Wang, Wan-Lun & Fan, Tsai-Hung, 2012. "Bayesian analysis of multivariate t linear mixed models using a combination of IBF and Gibbs samplers," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 300-310.
    2. Kuo, Kun-Lin & Song, Chwan-Chin & Jiang, Thomas J., 2017. "Exactly and almost compatible joint distributions for high-dimensional discrete conditional distributions," Journal of Multivariate Analysis, Elsevier, vol. 157(C), pages 115-123.
    3. Jun Yang & Guohua Zou & Yu Zhao, 2008. "Two noniterative algorithms for computing posteriors," Computational Statistics, Springer, vol. 23(3), pages 443-453, July.

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