Gaussian predictive process models for large spatial data sets

Authors: Banerjee, Sudipto¹; Gelfand, Alan E.²; Finley, Andrew O.³; Sang, Huiyan²

Source: Journal of the Royal Statistical Society: Series B (Statistical Methodology), Volume 70, Number 4, September 2008 , pp. 825-848(24)

Publisher: Wiley-Blackwell

Buy & download fulltext article:

Price: $48.00 plus tax (Refund Policy)

Abstract:

Summary.

With scientific data available at geocoded locations, investigators are increasingly turning to spatial process models for carrying out statistical inference. Over the last decade, hierarchical models implemented through Markov chain Monte Carlo methods have become especially popular for spatial modelling, given their flexibility and power to fit models that would be infeasible with classical methods as well as their avoidance of possibly inappropriate asymptotics. However, fitting hierarchical spatial models often involves expensive matrix decompositions whose computational complexity increases in cubic order with the number of spatial locations, rendering such models infeasible for large spatial data sets. This computational burden is exacerbated in multivariate settings with several spatially dependent response variables. It is also aggravated when data are collected at frequent time points and spatiotemporal process models are used. With regard to this challenge, our contribution is to work with what we call predictive process models for spatial and spatiotemporal data. Every spatial (or spatiotemporal) process induces a predictive process model (in fact, arbitrarily many of them). The latter models project process realizations of the former to a lower dimensional subspace, thereby reducing the computational burden. Hence, we achieve the flexibility to accommodate non-stationary, non-Gaussian, possibly multivariate, possibly spatiotemporal processes in the context of large data sets. We discuss attractive theoretical properties of these predictive processes. We also provide a computational template encompassing these diverse settings. Finally, we illustrate the approach with simulated and real data sets.

Keywords: Co-regionalization; Gaussian processes; Hierarchical modelling; Kriging; Markov chain Monte Carlo methods; Multivariate spatial processes; Space-time processes

Document Type: Research article

DOI: http://dx.doi.org/10.1111/j.1467-9868.2008.00663.x

Affiliations: 1: University of Minnesota, Minneapolis, USA 2: Duke University, Durham, USA 3: Michigan State University, East Lansing, USA

Publication date: 2008-09-01

Gaussian predictive process models for large spatial data sets

Buy & download fulltext article:

Tools

Key

Text size:

Useful pages