Hyper Markov Laws for Correlation Matrices

• Activity Number: 313
• Type: Contributed
• Date/Time: Tuesday, August 11, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Jeremy Gaskins*
• Companies: University of Louisville
• Keywords: Dependence ; Graphical model ; Sparsity ; Hyper inverse Wishart

Abstract

Parsimoniously modeling the dependence structure of multivariate data is often a challenging task, particularly if the dependence parameter is a correlation matrix due to modeling assumptions or identifiability constraints. In this work, we connect the powerful techniques of graphical models and the hyper inverse Wishart distribution to produce hyper Markov priors for correlation matrices. The priors are formed by the Markov combination of the (marginal) distribution of a correlation matrix from an inverse Wishart or Wishart prior. These priors produce a sparse correlation matrix with zero elements in its inverse whenever variables are conditionally independent. An MCMC scheme to obtain posterior inference is introduced, and the performance is considered using a simulation study and a financial data example.