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With continued advances in Geographic Information Systems and related computational technologies, statisticians are often required to analyze very large spatial data sets. This has generated substantial interest over the last decade, already too vast to be summarized here, in scalable methodologies for analyzing large spatial data sets. Scalable spatial process models have been found especially attractive due to their richness and flexibility and, particularly so in the Bayesian paradigm, due to their presence in hierarchical model settings. However, the vast majority of research articles present in this domain have been geared toward innovative theory or more complex model development. Very limited attention has been accorded to approaches for easily implementable scalable hierarchical models for the practicing scientist or spatial analyst. This article devises massively scalable Bayesian approaches that can rapidly deliver inference on spatial process that are practically indistinguishable from inference obtained using more expensive alternatives. A key emphasis is on implementation within very standard (modest) computing environments (eg, a standard desktop or laptop) using easily available statistical software packages. Key insights are offered regarding assumptions and approximations concerning practical efficiency .

Practical Bayesian modeling and inference for massive spatial data sets on modest computing environments †