Random fields for spatial data modeling: a primer for scientists and engineers

by Hristopulos, Dionissios T.

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Title Statements

Full title :Random fields for spatial data modeling : a primer for scientists and engineers / Dionissios T. Hristopulos.

Summary

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 e

Edition Statements

Publication Date:2020

Publication Statements

Publisher(s):Springer
Place of Publication:Dordrecht
Language:eng
Publication Date:2020

The Physical Object

Description:xxx, 867 páginas : : ilustraciones ; : 24 cm

Edition Identifiers

oclc:on1319459626

Introduction -- Preliminary Remarks -- Why Random Fields? -- Notation and Definitions -- Noise and Errors -- Spatial Data and Basic Processing Procedures -- A Personal Selection of Relevant Books -- Trend Models and Estimation -- Empirical Trend Estimation -- Regression Analysis -- Global Trend Models -- Local Trend Models -- Trend Estimation based on Physical Information -- Trend Based on the Laplace Equation -- Basic Notions of Random Fields -- Introduction -- Single-Point Description -- Stationarity and Statistical Homogeneity -- Variogram versus Covariance -- Permissibility of Covariance Functions -- Permissibility of Variogram Functions -- Additional Topics of Random Field Modeling -- Ergodicity -- Statistical Isotropy -- Anisotropy -- Anisotropic Spectral Densities -- Multipoint Description of Random Fields -- Geometric Properties of Random Fields -- Local Properties -- Covariance Hessian Identity and Geometric Anisotropy -- Spectral Moments --