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Activity Number: 101
Type: Invited
Date/Time: Monday, August 5, 2013 : 8:30 AM to 10:20 AM
Sponsor: Section on Statistics and the Environment
Abstract - #307021
Title: Nonstationary and Nonparametric Modeling of Multivariate Spatial Processes
Author(s): Montserrat Fuentes*+ and Brian J. Reich
Companies: North Carolina State University and North Carolina State University
Keywords: Nonparametric Bayes ; Spatial statistics ; Air pollution ; Nonstationary covariance ; Multivariate statistics ; nonseparable models
Abstract:

We introduce a nonparametric multivariate spatial model that avoids specifying a Gaussian distribution for spatial random effects. The stick-breaking prior is extended here to the spatial setting by assigning each location a different, unknown distribution, and smoothing the distributions in space with a series of space-dependent kernel functions that have a space-varying bandwidth parameter. This results in a flexible nonstationary spatial model, as different kernel functions lead to different relationships between the distributions at nearby locations. We extend the model to the multivariate setting by having for each process a different kernel function, but sharing the location of the kernel knots across the different processes. The resulting covariance for the multivariate process is in general nonstationary and nonseparable. The modelling framework proposed here is also computationally efficient because it avoids inverting large matrices and calculating determinants. The methods are illustrated using simulated examples and an air pollution application to model components of fine particulate matter.


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