Daniel Kirsner and Bruno Sanso
04/17/2019 10:25 AM
Statistics
Large spatial datasets often have fine scale features that only
occur in sub-domains of the space, coupled with large scale
features at much larger ranges. We develop a multi-scale spatial
kernel convolution model where fine scale local features are
captured by high resolution knots while lower resolution terms
are used to describe large scale features. To achieve parsimony and
explicitly identify the sub-domains of the space that exhibit fine
scale attributes, we develop a form of shotgun stochastic search
coupled with a stochastic process prior that induces structured sparsity that results in spatially varying resolution.
In contrast to existing approaches, our approach does not require
Markov chain Monte Carlo. In addition, the model does not require the
spatially varying maximum resolution to be specified in advance.
Our 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, and
it is possible to leverage the availability of convenient formulas for
updating the coefficients when a single new knot is
added. Competitive performance for
computations, prediction, and interval estimation is demonstrated
using simulation experiments and real data. Supplementary material for this article is available online.
