Multi-scale shotgun stochastic search for large spatial datasets

Large spatial datasets often exhibit fine scale features that only occur in sub-domains of the space, coupled with large scale features at much larger ranges. A multi-scale spatial kernel convolution model is developed where fine scale local features are captured by high resolution knots while lower resolution terms are used to describe large scale features. This method achieves parsimony and explicitly identifies the sub-domains of the space that exhibit fine scale attributes by using a form of shotgun stochastic search coupled with a stochastic process prior that induces structured sparsity resulting in spatially varying resolution. In contrast to existing approaches, this approach does not require Markov chain Monte Carlo to produce a fully probabilistic quantification of the prediction uncertainty. In addition, the model does not require a maximum resolution to be specified in advance. The model fitting approach, based on Bayesian model averaging, is computationally feasible on large datasets, as computations for shotgun stochastic search can be performed in parallel, leveraging the availability of convenient formulas for fast updating the coefficients when adding a single knot. Competitive performance for computations, prediction, and interval estimation is demonstrated using simulation experiments and real data.