Abstract #300750

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JSM 2003 Abstract #300750
Activity Number: 43
Type: Topic Contributed
Date/Time: Sunday, August 3, 2003 : 4:00 PM to 5:50 PM
Sponsor: Section on Bayesian Stat. Sciences
Abstract - #300750
Title: A Sampling Algorithm for Correlation Matrices
Author(s): Xiao Zhang*+ and W. John Boscardin
Companies: University of California, Los Angeles and University of California, Los Angeles
Address: 3281 Sepulveda Blvd., Los Angeles, CA, 90034,
Keywords: Markov chain Monte Carlo ; Metropolis-Hastings algorithm ; Bayesian estimate ; multivariate probit model ; Wishart distribution
Abstract:

We demonstrate a Metropolis-Hastings algorithm for sampling from the posterior distribution of a correlation matrix. A density supported on the space of all positive definite correlation matrices is obtained by integrating out the variance components of a variance-covariance matrix which follows a Wishart distribution. We then incorporate this correlation distribution into a Metropolis-Hastings algorithm producing candidates that are always proper correlation matrices. Variants of this distribution can be used to create families of prior distributions for correlation matrices. The methodology is illustrated through a simulated example and applications to data from psychiatry and neuroscience studies.

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