Intrinsic autoregressions at multiple resolutions |
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| Institution: | 1. Department of Mathematics, Imperial College, 180 Queen''s Gate, London SW7 2BZ, UK;2. Duke University, ISDS, Box 90251, Durham, NC 27708-0251, USA;1. Department of Gastroenterology and Hepatology, Academic Medical Center, Amsterdam, The Netherlands;2. Laboratory of Microbiology, Wageningen University, Wageningen, The Netherlands;3. Department of Cardiology, Academic Medical Center, Amsterdam, The Netherlands;4. Departments of Bacteriology and Immunology and Veterinary Biosciences, University of Helsinki, Finland;1. Auckland Bioengineering Institute, University of Auckland, Auckland, New Zealand;2. Department of Surgery, Vanderbilt University, Nashville, Tennessee;3. Department of Surgery, University of Auckland, Auckland, New Zealand;4. Division of Gastroenterology and Hepatology, Enteric Neurosciences Program, Mayo Clinic, Rochester, Minnesota;5. Histology and Embryology Research Unit, Department of Experimental and Clinical Medicine, University of Florence, Florence, Italy;6. Department of Surgery, Mississippi Medical Center, Jackson, Mississippi;7. Department of Gastroenterology, University of Louisville, Louisville, Kentucky;1. Department of Medicine, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina;2. Departments of Molecular Virology and Microbiology and Medicine-GI, Baylor College of Medicine, Houston, Texas |
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| Abstract: | 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. |
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