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 posteriordistribution 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.
Bruno Sansó is Professor, Department Statistics, University of California Santa Cruz. Sansó's PhD is from Universidad Central de Venezuela, 1992. He is an expert in Bayesian hierarchical models for spatio-temporal models, extreme values, computer model emulation and calibration, and point processes. His work focuses on environmental and climatological applications. Sansó was Professor and co-founder of the Department of Scientific Computing and Statistics, Universidad Simón Bolívar, Venezuela. In 2001 he joined the University of California Santa Cruz Department of Applied Mathematics and Statics, being department chair during 2009-2014. He has supervised many graduate students. One of them won the Savage Award in 2010. Sansó's publications have appeared in the most highly ranked statistical journals, obtaining some prestigious awards, like the Mitchell Prize in 2009 and 2019. Sansó was Associate Editor of JSPI and Technometrics. He was Editor in Chief of the journal Bayesian Analysis. He has had appointed and elected leadership roles in the American Statistical Association, the International Environmetrics Society, The Bernoulli Society and the International Society for Bayesian Analysis. Sansó is Elected Member of the International Statistical Institute, Fellow of the American Statistical Association, and Fellow of the International Society for Bayesian Analysis.