Space-varying regression models are generalizations of standard linear models where the regression coe cients are allowed to change in space. The spatial structure is speciÿed by a multivariate extension of pairwise di erence priors, thus enabling incorporation of neighboring structures and easy sampling schemes. Bayesian inference is performed by incorporation of a prior distribution for the hyperparameters. This approach leads to an untractable posterior distribution. Inference is approximated by drawing samples from the posterior distribution. Di erent sampling schemes are available and may be used in an MCMC algorithm. They basically di er in the way they handle blocks of regression coe cients. Approaches vary from sampling each location-speciÿc vector of coe cients to complete elimination of all regression coe cients by analytical integration. These schemes are compared in terms of their computation, chain autocorrelation, and resulting inference. Results are illustrated with simulated data and applied to a real dataset. Related prior speciÿcations that can accommodate the spatial structure in di erent forms are also discussed. The paper concludes with a few general remarks.

Bayesian paradigm, Conditional autoregressive priors, Monte Carlo Markov chain, Stochastic frontier models, Spatial econometrics, C01, C11,

This paper describes the inference procedures required to perform Bayesian inference to some multivariate econometric models. These models have a spatial component built into commonly used multivariate models. In particular, the common component models are addressed and extended to accommodate for spatial dependence. Inference procedures are based on a variety of simulation-based schemes designed to obtain samples from the posterior distribution of model parameters. They are also used to provide a basis to forecast new observations. r 2004 Elsevier Inc. All rights reserved.

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