JSM 2004 - Toronto

Abstract #301736

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Activity Number: 436
Type: Contributed
Date/Time: Thursday, August 12, 2004 : 10:30 AM to 12:20 PM
Sponsor: Section on Bayesian Statistical Science
Abstract - #301736
Title: Bayesian Estimation of a Covariance Matrix with Applications on Mixed Effects Models
Author(s): John S.J. Hsu*+ and Steven C.W. Hsu
Companies: University of California, Santa Barbara and National College of Physical Education and Sports
Address: Dept. of Statistics and Applied Probability, Santa Barbara, CA, 93106,
Keywords: Laplacian approximation ; hierarchical Bayes ; Metropolis-Hastings MCMC algorithm
Abstract:

Leonard and Hsu (1992) suggested a flexible class of prior distributions for the covariance matrix of a multivariate normal distribution. They proposed a normal prior on the log-covariance matrix and calculated the exact posterior moments using importance sampling methods. We propose a Laplacian approximation to the posterior moments. The approximation is reasonably accurate when compared with the exact result, and the calculation takes only seconds of computer time. We further consider the same prior structure for the covariance matrix in the mixed effects model. Exact posterior moments for the parameters in the model can be calculated via a Metropolis-Hastings MCMC algorithm. A subset of the High School and Beyond survey data is analyzed and will be reported.

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