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.

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 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...