On Monte Carlo methods for Bayesian multivariate regression models with heavy-tailed errors

We consider Bayesian analysis of data from multivariate linear regression models whose errors have a distribution that is a scale mixture of normals. Such models are used to analyze data on financial returns, which are notoriously heavy-tailed. Let π denote the intractable posterior density that results when this regression model is combined with the standard non-informative prior on the unknown regression coefficients and scale matrix of the errors. Roughly speaking, the posterior is proper if and only if n ≥ d + k, where n is the sample size, d is the dimension of the response, and k is number of covariates. We provide a method of making exact draws from π in the special case where n = d + k, and we study Markov chain Monte Carlo (MCMC) algorithms that can be used to explore π when n > d + k. In particular, we show how the Haar PX-DA technology studied in Hobert and Marchev (2008) can be used to improve upon Liu’s (1996) data augmentation (DA) algorithm. Indeed, the new ...

• Type: Journal
• Year: 2010
• Where: MA
• Authors: Vivekananda Roy, James P. Hobert
• Keywords: Algorithm, Communications, MA 2010, Markov Chain, Regression Model