Electronic Journal of Statistics
- Electron. J. Statist.
- Volume 7 (2013), 946-972.
Spatial models for point and areal data using Markov random fields on a fine grid
I consider the use of Markov random fields (MRFs) on a fine grid to represent latent spatial processes when modeling point-level and areal data, including situations with spatial misalignment. Point observations are related to the grid cell in which they reside, while areal observations are related to the (approximate) integral over the latent process within the area of interest. I review several approaches to specifying the neighborhood structure for constructing the MRF precision matrix, presenting results comparing these MRF representations analytically, in simulations, and in two examples. The results provide practical guidance for choosing a spatial process representation and highlight the importance of this choice. In particular, the results demonstrate that, and explain why, standard CAR models can behave strangely for point-level data. They show that various neighborhood weighting approaches based on higher-order neighbors that have been suggested for MRF models do not produce smooth fields, which raises doubts about their utility. Finally, they indicate that an MRF that approximates a thin plate spline compares favorably to standard CAR models and to kriging under many circumstances.
Electron. J. Statist., Volume 7 (2013), 946-972.
Received: May 2012
First available in Project Euclid: 15 April 2013
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Paciorek, Christopher J. Spatial models for point and areal data using Markov random fields on a fine grid. Electron. J. Statist. 7 (2013), 946--972. doi:10.1214/13-EJS791. https://projecteuclid.org/euclid.ejs/1366031046
- Supplementary data and R code. The supplementary materials contain the data for the PM example as well as R code for all analyses and figures.