Approximate Predictive Densities and Their Applications in Generalized Linear Models |
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Authors: | Chen Min Wang Xinlei |
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Affiliation: | a Department of Clinical Sciences, University of Texas Southwestern Medical Center, Dallas, TX 75390, United Statesb Department of Statistical Science, Southern Methodist University, 3225 Daniel Avenue, P O Box 750332, Dallas, TX 75275-0332, United States |
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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. |
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Keywords: | Laplace approximation GLM Normal prior Power prior Conjugate prior Asymptotic normality Logistic regression |
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