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Gaussian Markov Random Field (GMRF) models are most widely used in spatial statistics -a very active area of research in which few up-to-date reference works are available. Gaussian Markov Random Field: Theory and Applications is the first book on the subject that provides a unified framework of GMRFs with particular emphasis on the computational aspects. It includes extensive case studies and an online C-library for fast and exact simulation. With chapters contributed by leading researchers in the field, this volume is essential reading for statisticians working in spatial theory and its applications, as well as quantitative researchers in a wide range of fields in which spatial data analysis is important.

Gaussian Markov random fields.

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Markov random fields --- Markov random fields. --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Statistics --- 519.217 --- Markov processes --- 519.217 Markov processes --- Fields, Markov random --- Random fields

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Transfer functions --- Fonctions de transfert. --- Fourier transformations --- Fourier, Transformations de. --- Markov random fields --- Markov, Champs aléatoires de. --- Markov, Champs aléatoires de.

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This Special Issue of the journal Entropy, titled “Information Geometry I”, contains a collection of 17 papers concerning the foundations and applications of information geometry. Based on a geometrical interpretation of probability, information geometry has become a rich mathematical field employing the methods of differential geometry. It has numerous applications to data science, physics, and neuroscience. Presenting original research, yet written in an accessible, tutorial style, this collection of papers will be useful for scientists who are new to the field, while providing an excellent reference for the more experienced researcher. Several papers are written by authorities in the field, and topics cover the foundations of information geometry, as well as applications to statistics, Bayesian inference, machine learning, complex systems, physics, and neuroscience.

decomposable divergence --- tensor Sylvester matrix --- maximum pseudo-likelihood estimation --- matrix resultant --- ?) --- Markov random fields --- Fisher information --- Fisher information matrix --- Stein equation --- entropy --- Sylvester matrix --- information geometry --- stationary process --- (? --- dually flat structure --- information theory --- Bezout matrix --- Vandermonde matrix

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This Special Issue of the journal Entropy, titled “Information Geometry I”, contains a collection of 17 papers concerning the foundations and applications of information geometry. Based on a geometrical interpretation of probability, information geometry has become a rich mathematical field employing the methods of differential geometry. It has numerous applications to data science, physics, and neuroscience. Presenting original research, yet written in an accessible, tutorial style, this collection of papers will be useful for scientists who are new to the field, while providing an excellent reference for the more experienced researcher. Several papers are written by authorities in the field, and topics cover the foundations of information geometry, as well as applications to statistics, Bayesian inference, machine learning, complex systems, physics, and neuroscience.

decomposable divergence --- tensor Sylvester matrix --- maximum pseudo-likelihood estimation --- matrix resultant --- ?) --- Markov random fields --- Fisher information --- Fisher information matrix --- Stein equation --- entropy --- Sylvester matrix --- information geometry --- stationary process --- (? --- dually flat structure --- information theory --- Bezout matrix --- Vandermonde matrix