SLGP: An R Package for Spatial Conditional Density Estimation

Abstract

The SLGP package provides nonparametric estimation of fields of probability densities indexed by covariates, from unevenly sized samples with few or no replicates. A Spatial Logistic Gaussian Process applies a logistic density transformation to a finite-rank Gaussian process over a joint index-response domain, yielding a prior over conditional densities that adapts in location, shape, and modality. The contribution of this paper is the implementation: a finite-rank Random-Fourier-Feature representation that keeps the transformed process numerically tame, a log-concave likelihood that makes the fit a convex problem, and a family of quadrature shortcuts for the normalising integrals that turn a per-observation cost into a per-grid cost. Three estimation modes are available: MAP, Laplace, and full MCMC. We demonstrate the package throughout on the classical Fiji-Tonga earthquake catalogue, estimating how the distribution of hypocentre depths deforms across the region, and on a discrete-response variant.