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Approximate predictive densities and their applications in generalized linear models

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  • Chen, Min
  • Wang, Xinlei

Abstract

Exact calculations of model posterior probabilities or related quantities are often infeasible due to the analytical intractability of predictive densities. Here new approximations for obtaining predictive densities are proposed and contrasted with those based on the Laplace method. Our theory and a numerical study indicate that the proposed methods are easy to implement, computationally efficient, and accurate over a wide range of hyperparameters. In the context of GLMs, we show that they can be employed to facilitate the posterior computation under three general classes of informative priors on regression coefficients. A real example is provided to demonstrate the feasibility and usefulness of the proposed methods in a fully Bayes variable selection procedure.

Suggested Citation

  • Chen, Min & Wang, Xinlei, 2011. "Approximate predictive densities and their applications in generalized linear models," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1570-1580, April.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:4:p:1570-1580
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    References listed on IDEAS

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    1. Meyer M.C. & Laud P.W., 2002. "Predictive Variable Selection in Generalized Linear Models," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 859-871, September.
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    4. Boone, Edward L. & Ye, Keying & Smith, Eric P., 2005. "Assessment of two approximation methods for computing posterior model probabilities," Computational Statistics & Data Analysis, Elsevier, vol. 48(2), pages 221-234, February.
    5. Zellner, A., 1988. "Optimal Information-Processing And Bayes' Theorem," Papers m8803, Southern California - Department of Economics.
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