Inference for Bayesian

For spatial data modeled using the customary variogram approach, likelihood-based or fully Bayesian inference has been conceded as infeasible for large sample size n. The diiculty in such a setting is that modeling the variogram requires modeling the joint covariance structure. For the sample, this is captured as an n n covariance matrix. The computation of the likelihood then requires the inversion of. Moreover, implementation of usual iterative model tting requires repeated inversions of this matrix. When n is large, it may not be feasible to carry this out within practical time constraints. Even if we were to attempt it, the rounding error that results from performing so many arithmetic operations becomes an issue; we would have no conndence in the accuracy or stability of the resulting inverses. We propose to carry out such spatial modeling for large n by replacing matrix inversion with simulation using importance sampling. With polishing, this approach enables approximate Bayesian analysis of spatial data sets of much larger sizes than previously considered in the literature. We illustrate with an example involving the selling prices of 857 residential properties in Baton Rouge, LA.