Speaker: Chris Carter, Statistical and Applied Mathematical Sciences Institute, Duke University.
Abstract: This talk describes an efficient sampler for the Bayesian estimation of covariance matrices using Markov chain Monte Carlo (MCMC). The methods apply to decomposable covariance selection models with a hyper inverse Wishart (HIW) prior for the covariance matrix. The conjugate properties of the HIW distribution are used to generate from reduced conditional distributions. In particular, the covariance matrix is integrated out of all conditional distributions and is not generated in the MCMC. The resulting sampler is shown to have a much faster convergence rate than existing methods. The computational complexity of one iteration of the MCMC is shown to be similar to existing methods, so the gain in convergence rate is significant. An efficient mixture estimate of the posterior mean of the inverse covariance matrix is given.