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Nonparametric Bayesian models for a spatial covariance
Journal article   Peer reviewed

Nonparametric Bayesian models for a spatial covariance

Brian J Reich and Montserrat Fuentes
Statistical Methodology, Vol.9(1), pp.265-274
2012
DOI: 10.1016/j.stamet.2011.01.007
PMCID: PMC3743268
PMID: 23956705
url
https://www.ncbi.nlm.nih.gov/pmc/articles/3743268View
Open Access

Abstract

A crucial step in the analysis of spatial data is to estimate the spatial correlation function that determines the relationship between a spatial process at two locations. The standard approach to selecting the appropriate correlation function is to use prior knowledge or exploratory analysis, such as a variogram analysis, to select the correct parametric correlation function. Rather that selecting a particular parametric correlation function, we treat the covariance function as an unknown function to be estimated from the data. We propose a flexible prior for the correlation function to provide robustness to the choice of correlation function. We specify the prior for the correlation function using spectral methods and the Dirichlet process prior, which is a common prior for an unknown distribution function. Our model does not require Gaussian data or spatial locations on a regular grid. The approach is demonstrated using a simulation study as well as an analysis of California air pollution data.
Spectral density Particulate matter Covariance estimation Dirichlet process prior

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