vbid/9789402419184

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 ofmodels 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-Lo�ve expansion of the Spartan model.� The book will appeal to engineers, physicists, and geoscientists whose research involves spatial models or spatialdata 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.Typham this is the title: Random Fields for Spatial Data Modeling A Primer for Scientists and Engineers