This article is published in Environmetrics as a special issue on Spatio-Temporal Stochastic Modelling (METMAV), edited by Wenceslao González Manteiga, University of Santiago de Compostela, Spain.
Adaptive Gaussian predictive process models for large spatial datasets†
Version of Record online: 10 OCT 2011
Copyright © 2011 John Wiley & Sons, Ltd.
Volume 22, Issue 8, pages 997–1007, December 2011
How to Cite
Guhaniyogi, R., Finley, A. O., Banerjee, S. and Gelfand, A. E. (2011), Adaptive Gaussian predictive process models for large spatial datasets. Environmetrics, 22: 997–1007. doi: 10.1002/env.1131
- Issue online: 12 DEC 2011
- Version of Record online: 10 OCT 2011
- Manuscript Accepted: 25 JUL 2011
- Manuscript Revised: 22 JUL 2011
- Manuscript Received: 15 NOV 2010
- NSF-DMS-1106609 and NIH/NIGMS 1-RC1-GM092400-01
- US Forest Service Forest Inventory and Analysis National Program, Forest Health Technology Enterprise Team, and NASA Carbon Cycle Science. Grant Numbers: 04-0225-019, 08-AH-971
- NSF-CDI-0940671 and NSF-DMS-0914906
- Bayesian hierarchical models;
- Gaussian process;
- intensity surfaces;
- low-rank models;
- Markov chain Monte Carlo;
- predictive process
Large point referenced datasets occur frequently in the environmental and natural sciences. Use of Bayesian hierarchical spatial models for analyzing these datasets is undermined by onerous computational burdens associated with parameter estimation. Low-rank spatial process models attempt to resolve this problem by projecting spatial effects to a lower-dimensional subspace. This subspace is determined by a judicious choice of ‘knots’ or locations that are fixed a priori. One such representation yields a class of predictive process models (e.g., Banerjee et al., 2008) for spatial and spatial-temporal data. Our contribution here expands upon predictive process models with fixed knots to models that accommodate stochastic modeling of the knots. We view the knots as emerging from a point pattern and investigate how such adaptive specifications can yield more flexible hierarchical frameworks that lead to automated knot selection and substantial computational benefits. Copyright © 2011 John Wiley & Sons, Ltd.