We study MCMC algorithms for Bayesian analysis of a linear regression model with generalized hyperbolic errors. The Markov operators associated with the standard data augmentation algorithm and a sandwich variant of that algorithm are shown to be trace-class.

Gibbs samplers derived under different parametrizations of the target density can have radically different rates of convergence. In this article, we specify conditions under which reparametrization leaves the convergence rate of a Gibbs chain unchanged. An example illustrates how these results...

Let π denote the intractable posterior density that results when the standard default prior is placed on the parameters in a linear regression model with iid Laplace errors. We analyze the Markov chains underlying two different Markov chain Monte Carlo algorithms for exploring π. In...

Consider the quantile regression model Y=Xβ+σϵ where the components of ϵ are i.i.d. errors from the asymmetric Laplace distribution with rth quantile equal to 0, where r∈(0,1) is fixed. Kozumi and Kobayashi (2011) [9] introduced a Gibbs sampler that can be used to explore the intractable...

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 [pi] denote the intractable posterior density...

Every reversible Markov chain defines an operator whose spectrum encodes the convergenceproperties of the chain. When the state space is finite, the spectrum is just the set ofeigenvalues of the corresponding Markov transition matrix. However, when the state space isinfinite, the spectrum may be...

A new approach to clustering multivariate data, based on a multilevel linear mixed model, is proposed. A key feature of the model is that observations from the same cluster are correlated, because they share cluster-specific random effects. The inclusion of cluster-specific random effects allows...