Summary
Markov random field models are used to describe the distribution of spatially arranged random variables. When estimating the parameters of such models, usually second order stationarity is assumed, but often doubted in applications. We present an approach which allows for nonstationarities of the mean and the covariance. For this purpose spatially varying coefficients are introduced. In applications we obtained more appropriate models as well as further insight into the structure of spatial data. The Mercer and Hall wheat-yield data are presented as example.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
BESAG, J. E. (1974): Spatial interaction and the statistical analysis of lattice systems. J. R. Statist. Soc. B, 36, 192–225.
BESAG, J. E. (1975): Statistical analysis of non-lattice data. The Statistician, 24, 179–195.
BESAG, J. E. and MORAN, P. A. P. (1975): On the estimation and testing of spatial interaction in Gaussian lattice processes. Biometrika, 62, 552–562.
CLEVELAND, W. S. (1979): Robust locally weighted regression and smoothing scatterplots. J. Amer. Statist. Assoc., 74, 829–836.
CRESSIE, N. (1993): Statistics for spatial data. Revised edition, Wiley, New York.
GEYER, C. (1991): Markov chain Monte Carlo maximum likelihood. In: E. M. Keramidas (ed.): Comput. Sci. Statist. Proc. 23rd Symp. Interface, 156-163.
HASTIE, T. and TIBSHIRANI, R. (1993): Varying-coefficient models. J. R. Statist. Soc. B, 55, 757–796.
MERCER, W. B. and HALL, A. D. (1911): The experimental error of field trials. J. Agric. Sci., 4, 107–132.
STANISWALIS, J. (1989): The kernel estimate of a regression function in likelihood-based models. J. Amer. Statist. Assoc., 84, 276–283.
TIBSHIRANI, R. and HASTIE, T. (1987): Local likelihood estimation. J. Amer. Statist. Assoc., 82, 559–567.
VAN DER LINDE, A. (1994): On cross-validation for smoothing splines in the case of dependent observations. Austral. J. Statist., 36(1), 67–73.
WHITTLE, P. (1954): On stationary processes in the plane. Biometrika, 41, 434–449.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Dreesman, J. (1997). Markov Random Field Models with Spatially Varying Coefficients. In: Klar, R., Opitz, O. (eds) Classification and Knowledge Organization. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59051-1_15
Download citation
DOI: https://doi.org/10.1007/978-3-642-59051-1_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-62981-8
Online ISBN: 978-3-642-59051-1
eBook Packages: Springer Book Archive