Space-varying regression models: Specifications and simulation

Space-varying regression models are generalizations of standard linear models where the regression coefficients are allowed to change in space. The spatial structure is specified by a multivariate extension of pairwise difference 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. Different sampling schemes are available and may be used in an MCMC algorithm. They basically differ in the way they handle blocks of regression coefficients. Approaches vary from sampling each location- specific vector of coefficients to complete elimination of all regression coefficients 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 specifications that can accommodate the spatial structure in different forms are also discussed. The paper concludes with a few general remarks.