Slepian models for Gaussian random landscapes

Gaussian random field models for spatial data

Spatial data contain information about both the attribute of interest as well as its location. Examples can be found in a large number of disciplines including ecology, geology, epidemiology, geography, image analysis, meteorology, forestry, and geosciences. The location may be a set of coordinates, such as the latitude and longitude associated with an observed pollutant level, or it may be a s...

Small Ball Probabilities for the Slepian Gaussian Fields

The d-dimensional Slepian Gaussian random field {S(t), t ∈ R+} is a mean zero Gaussian process with covariance function ES(s)S(t) = ∏d i=1 max(0, ai − |si − ti|) for ai > 0 and t = (t1, · · · , td) ∈ R+. Small ball probabilities for S(t) are obtained under the L2-norm on [0, 1]d, and under the sup-norm on [0, 1]2 which implies Talagrand’s result for the Brownian sheet. The method of proof for t...

Autoregressive Gaussian Random Vectors of First Order

Parameter Estimation in Spatial Generalized Linear Mixed Models with Skew Gaussian Random Effects using Laplace Approximation

 Spatial generalized linear mixed models are used commonly for modelling non-Gaussian discrete spatial responses. We present an algorithm for parameter estimation of the models using Laplace approximation of likelihood function. In these models, the spatial correlation structure of data is carried out by random effects or latent variables. In most spatial analysis, it is assumed that rando...

Multivariate latent Gaussian random field mixture models