First-order intrinsic autoregressions and the de Wijs process
We discuss intrinsic autoregressions for a first-order neighbourhood on a two-dimensional rectangular lattice and give an exact formula for the variogram that extends known results to the asymmetric case. We obtain a corresponding asymptotic expansion that is more accurate and more general than prev...
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| Veröffentlicht in: | Biometrika 2005-12, Vol.92 (4), p.909-920 |
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| container_title | Biometrika |
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| creator | Besag, Julian Mondal, Debashis |
| description | We discuss intrinsic autoregressions for a first-order neighbourhood on a two-dimensional rectangular lattice and give an exact formula for the variogram that extends known results to the asymmetric case. We obtain a corresponding asymptotic expansion that is more accurate and more general than previous ones and use this to derive the de Wijs variogram under appropriate averaging, a result that can be interpreted as a two-dimensional spatial analogue of Brownian motion obtained as the limit of a random walk in one dimension. This provides a bridge between geostatistics, where the de Wijs process was once the most popular formulation, and Markov random fields, and also explains why statistical analysis using intrinsic autoregressions is usually robust to changes of scale. We briefly describe corresponding calculations in the frequency domain, including limiting results for higher-order autoregressions. The paper closes with some practical considerations, including applications to irregularly-spaced data. |
| doi_str_mv | 10.1093/biomet/92.4.909 |
| format | Article |
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| ispartof | Biometrika, 2005-12, Vol.92 (4), p.909-920 |
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| language | eng |
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| source | RePEc; JSTOR Mathematics & Statistics; Jstor Complete Legacy; Oxford University Press Journals All Titles (1996-Current) |
| subjects | Agricultural field trial Agriculture Applications Approximation Asymptotic expansion Biology, psychology, social sciences De Wijs process Earth science Environmetrics Epidemiology Error rates Exact sciences and technology Geographical epidemiology Geostatistics Inference from stochastic processes time series analysis Intrinsic autoregression Markov processes Markov random field Mathematical functions Mathematical lattices Mathematics Medical sciences Probability and statistics Probability theory and stochastic processes Regression analysis Sciences and techniques of general use Special processes (renewal theory, markov renewal processes, semi-markov processes, statistical mechanics type models, applications) Spectral energy distribution Statistical analysis Statistics Variogram White noise |
| title | First-order intrinsic autoregressions and the de Wijs process |
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