Dobrin Marchev
Department of Statistics
University of Florida
Monte Carlo Methods for Posterior Distributions Associated with
Multivariate Student's t Data
Let p denote the intractable posterior distribution that results when a
random sample of size n from a d-dimensional location-scale Student's t
distribution (with v degrees of freedom) is combined with the standard
non-informative prior. We consider several Monte Carlo methods for sampling
from p, including rejection samplers and Gibbs samplers. Special attention
is paid to the Markov chain Monte Carlo algorithm developed by van Dyk and
Meng (JCGS, 2001) who provided considerable empirical evidence that their
algorithm converges to stationarity much faster than the standard Gibbs
sampler. We formally analyze the Markov chain underlying van Dyk and Meng's
algorithm and conclude that for many (d,v,n) triples, it is geometrically
ergodic.
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