This paper extends Besag's (1994) identifiability conditions to propose convergence conditions for the Gibbs sampler that are independent of the selected version of the conditional distributions. Moreover, we show that the support of the joint distribution must be connected if the Gibbs sampler...

Let "π" denote an intractable probability distribution that we would like to explore. Suppose that we have a positive recurrent, irreducible Markov chain that satisfies a minorization condition and has "π" as its invariant measure. We provide a method of using simulations from the Markov chain...

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...

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.

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...

Consider a probit regression problem in which "Y"₁, …, "Y"_"n" are independent Bernoulli random variables such that <formula format="inline"><file name="rssb_602_mu1.gif" type="gif" /></formula> where "x"_"i" is a "p"-dimensional vector of known covariates that are associated with "Y"_"i", "&bgr;" is a "p"-dimensional vector of unknown regression coefficients and Φ(·)...

We consider fixed scan Gibbs and block Gibbs samplers for a Bayesian hierarchical random effects model with proper conjugate priors. A drift condition given in Meyn and Tweedie (1993, Chapter 15) is used to show that these Markov chains are geometrically ergodic. Showing that a Gibbs sampler is...

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...