A New Prior for the Unconditioned Covariance Matrix

• Activity Number: 298
• Type: Contributed
• Date/Time: Tuesday, August 2, 2011 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Samprit Banerjee*+ and Stefano Monni
• Companies: Weill Cornell Medical College and Weill Cornell Medical College
• Keywords: covariance matrix ; reference prior ; high dimensional ; hit and run

Abstract

Estimation of the covariance matrix, especially in higher dimensions ("large p small n") is a challenging statistical problem which is of great interest in many applications. It is well known that the sample covariance matrix is a poor estimator even for moderately high p. The currently accepted best estimator for the unconditioned covariance matrix is that based on the reference prior. We propose a new prior (reference-like) and demonstrate the improved estimation for higher dimensional matrices via simulations. We provide a Markov Chain Monte Carlo algorithm to implement the computation and highlight key aspects required to sample efficiently.