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Intrinsic autoregressions at multiple resolutions. (English) Zbl 1066.62093

Summary: We consider intrinsic autoregression models at multiple resolutions. Firstly, we describe a method to construct a class of approximately coherent Markov random fields (MRF) at different scales, overcoming the problem that the marginal Gaussian MRF is not, in general, a MRF with respect to any non-trivial neighbourhood structure. This is based on the approximation of non-Markov Gaussian fields as Gaussian MRFs and is optimal according to different theoretic notions such as Kullback-Leibler divergence. We extend the method to intrinsic autoregressions providing a novel multi-resolution framework.

MSC:

62M40 Random fields; image analysis
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62M30 Inference from spatial processes
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