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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 particular, it is shown that the Markov operators associated with the data augmentation (DA) algorithm and a sandwich variant are both trace-class. Consequently, both Markov chains are geometrically ergodic. It is also established that for each i ∈ {1, 2, 3,...}, the ith largest eigenvalue of the sandwich operator is less than or equal to the corresponding eigenvalue of the DA operator. It follows that the sandwich algorithm converges at least as fast as the DA algorithm. AMS 2000 subject classifications. Primary 60J27; secondary 62F15 Abbreviated title. MCMC algorithms for Bayesian linear regression

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.

Our goal is to introduce some of the tools useful for analyzing the output of a Markov chain Monte Carlo (MCMC) simulation. In particular, we focus on methods which allow the practitioner (and others!) to have confidence in the claims put forward. The following are the main issues we will address: (1) initial graphical assessment of MCMC output; (2)

The errors in a standard linear regression model are iid with common density 1σφ ε

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