A Prior for Partial Autocorrelation Selection

• Activity Number: 352
• Type: Contributed
• Date/Time: Tuesday, July 31, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Jeremy Gaskins*+ and Michael Daniels
• Companies: University of Florida and University of Florida
• Keywords: correlation matrix ; longitudinal data ; Bayesian methods ; covariance selection ; partial autocorrelations

Abstract

Modeling a correlation matrix can be a difficult statistical task due to the positive definite and unit diagonal constraints. Because the number of parameters increases quadratically in the dimension, it is often useful to consider a sparse parameterization. We introduce a prior on the set of correlation matrices through the set of partial autocorrelations (PACs), each of which vary independently over [-1,1]. The prior for each PAC is a mixture of a zero point mass and a continuous piece, allowing for a sparse representation. The structure implied under our prior is interpretable because each zero PAC implies a conditional independence relationship in the data distribution. The PAC priors are compared to standard methods through a simulation study and a multivariate probit data example.