Workshop SDS: Registration
View Submission - SDS2022
Title: Nearest neighbors processes for non-Gaussian geostatistical data Authors:  Bruno Sanso - University of California Santa Cruz (United States) [presenting]
Xiaotian Zheng - University of California Santa Cruz (United States)
Thanasis Kottas - University of California Santa Cruz (United States)
Abstract: A framework is presented 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 a distribution can be spatially varying, to capture non-homogeneous spatial features. The mixture structure of the model allows for efficient MCMC-based exploration of the posterior distribution of the model parameters, even for a relatively large number of locations. We illustrate the capabilities of NNMPs with observations corresponding to distributions with different non-Gaussiancharacteristics: Long tails; Compact support; skewness. We extend NNMPs to tackle discrete-valued distributions using a 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.