Bruno Sansó, UC Santa Cruz
Non-Gaussian geostatistical models using nearest neighbors processes
We present a framework for non-Gaussian spatial processes that encompasses large distribution families. Spatial dependence for a set of irregularly scattered locations is described with a mixture of pairwise kernels. Focusing on the nearest neighbors of a given location, within a reference set, we obtain a valid spatial process: the nearest neighbor mixture transition distribution process (NNMP). We develop conditions to construct general NNMP models with arbitrary pre-specified marginal distributions. Essentially, NNMPs are specified by a bi-variate distribution, with suitable marginals, used to specify the mixture transition kernels. Such distribution can be spatially varying, to capture non-homogeneous spatial features. The mixture structure of the model allows for efficient MCMC-based exploration of posterior distribution of the model parameters, even for relatively large number of locations. We illustrate the capabilities of NNMPs with observations corresponding to distributions with different non-Gaussian characteristics: Long tails; Compact support; skewness. We extend NNMPs to tackle discrete-valued distributions using continuous extension for the discrete bivariate copulas to enhance computational efficiency and stability. We illustrate the discrete NNMP with data corresponding to counts from the North American Bird Survey.