Modelling Gaussian Fields and Geostatistical Data Using Gaussian Markov Random Fields PDF Download

Author: Eva Vivalt
Publisher:
ISBN:
Category :
Languages : en
Pages : 138

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Author: Havard Rue
Publisher: CRC Press
ISBN: 0203492021
Category : Mathematics
Languages : en
Pages : 280

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Book Description
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. This is the first book on the subject that provides a unified framework of GMRFs with particular emphasis on the computational aspects. This book includes extensive case-studie

Author: Dionissios T. Hristopulos
Publisher: Springer Nature
ISBN: 9402419187
Category : Science
Languages : en
Pages : 884

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Book Description
This book provides an inter-disciplinary introduction to the theory of random fields and its applications. Spatial models and spatial data analysis are integral parts of many scientific and engineering disciplines. Random fields provide a general theoretical framework for the development of spatial models and their applications in data analysis. The contents of the book include topics from classical statistics and random field theory (regression models, Gaussian random fields, stationarity, correlation functions) spatial statistics (variogram estimation, model inference, kriging-based prediction) and statistical physics (fractals, Ising model, simulated annealing, maximum entropy, functional integral representations, perturbation and variational methods). The book also explores links between random fields, Gaussian processes and neural networks used in machine learning. Connections with applied mathematics are highlighted by means of models based on stochastic partial differential equations. An interlude on autoregressive time series provides useful lower-dimensional analogies and a connection with the classical linear harmonic oscillator. Other chapters focus on non-Gaussian random fields and stochastic simulation methods. The book also presents results based on the author’s research on Spartan random fields that were inspired by statistical field theories originating in physics. The equivalence of the one-dimensional Spartan random field model with the classical, linear, damped harmonic oscillator driven by white noise is highlighted. Ideas with potentially significant computational gains for the processing of big spatial data are presented and discussed. The final chapter concludes with a description of the Karhunen-Loève expansion of the Spartan model. The book will appeal to engineers, physicists, and geoscientists whose research involves spatial models or spatial data analysis. Anyone with background in probability and statistics can read at least parts of the book. Some chapters will be easier to understand by readers familiar with differential equations and Fourier transforms.

Author:
Publisher:
ISBN:
Category :
Languages : en
Pages :

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Gaussian geostatistical models (GGMs) and Gaussian Markov random fields (GMRFs) are two distinct approaches commonly used in modeling point referenced and areal data, respectively. In this dissertation, the relations between GMRFs and GGMs are explored based on approximations of GMRFs by GGMs, and vice versa. The proposed framework for the comparison of GGMS and GMRFs is based on minimizing the distance between the corresponding spectral density functions. In particular, the Kullback-Leibler discrepancy of spectral densities and the chi-squared distance between spectral densities are used as the metrics for the approximation. The proposed methodology is illustrated using empirical studies. As a part of application, we model associations between speciated fine particulate matter (PM) and mortality. Mortality counts and PM are obtained at county and point levels, respectively. To combine the variables with different spatial resolutions, we aggregate PM to the county level. The aggregated PM are modeled using GMRFs, and associations between PM and mortality are investigated based on Bayesian hierarchical spatio-temporal framework. This model is applied to speciated PM[subscript 2.5] and monthly mortality counts over the entire U.S. region for 1999-2000. We obtain high relative risks of mortality associated to PM[subscript 2.5] in the Eastern and Southern California area. Particularly, NO3 and crustal materials have greater health effects in the Western U.S., while SO4 and NH4 have more of an impact in the Eastern U.S. We show that the average risk associated with PM[subscript 2.5] is approximately twice what we obtained for PM10.

Author: Hae-Ryoung Song
Publisher:
ISBN:
Category :
Languages : en
Pages : 74

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Keywords: Gaussian Markov random, particulate matter, human health, Gaussian geostatistical models.

Author: Xavier Guyon
Publisher: Springer Science & Business Media
ISBN: 9780387944289
Category : Mathematics
Languages : en
Pages : 294

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Book Description
The theory of spatial models over lattices, or random fields as they are known, has developed significantly over recent years. This book provides a graduate-level introduction to the subject which assumes only a basic knowledge of probability and statistics, finite Markov chains, and the spectral theory of second-order processes. A particular strength of this book is its emphasis on examples - both to motivate the theory which is being developed, and to demonstrate the applications which range from statistical mechanics to image analysis and from statistics to stochastic algorithms.

Author: Rama Chellappa
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 608

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Introduces the theory and application of Markov random fields in image processing/computer vision. Modelling images through the local interaction of Markov models produces algorithms for use in texture analysis, image synthesis, restoration, segmentation and surface reconstruction.

Author: Robert J. Adler
Publisher: SIAM
ISBN: 0898716934
Category : Mathematics
Languages : en
Pages : 295

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Book Description
An important treatment of the geometric properties of sets generated by random fields, including a comprehensive treatment of the mathematical basics of random fields in general. It is a standard reference for all researchers with an interest in random fields, whether they be theoreticians or come from applied areas.

Author: Jessica Lyn Olsen
Publisher:
ISBN:
Category : Electronic dissertations
Languages : en
Pages : 44

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Book Description
Recently, Bayesian methods have become the essence of modern statistics, specifically, the ability to incorporate hierarchical models. In particular, correlated data, such as the data found in spatial and temporal applications, have benefited greatly from the development and application of Bayesian statistics. One particular application of Bayesian modeling is Gaussian Markov Random Fields. These methods have proven to be very useful in providing a framework for correlated data. I will demonstrate the power of GMRFs by applying this method to two sets of data; a set of temporal data involving car accidents in the UK and a set of spatial data involving Provo area apartment complexes. For the first set of data, I will examine how including a seatbelt covariate effects our estimates for the number of car accidents. In the second set of data, we will scrutinize the effect of BYU approval on apartment complexes. In both applications we will investigate Laplacian approximations when normal distribution assumptions do not hold.

Author: Emilio Porcu
Publisher: Springer Science & Business Media
ISBN: 3642170854
Category : Mathematics
Languages : en
Pages : 263

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Book Description
This book arises from the International Spring School "Advances and Challenges in Space-Time modelling of Natural Events," which took place March 2010. It details recent developments, new methods and applications in spatial statistics and related areas. This book arises from the International Spring School "Advances and Challenges in Space-Time modelling of Natural Events," which took place March 2010. It details recent developments, new methods and applications in spatial statistics and related areas.