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2010
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On Monte Carlo methods for Bayesian multivariate regression models with heavy-tailed errors

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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 ...
Vivekananda Roy, James P. Hobert
Added 29 Jan 2011
Updated 29 Jan 2011
Type Journal
Year 2010
Where MA
Authors Vivekananda Roy, James P. Hobert
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