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Books > Science & Mathematics > Mathematics > Probability & statistics
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Random Fields for Spatial Data Modeling - A Primer for Scientists and Engineers (Hardcover, 1st ed. 2020)
Loot Price: R3,234
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Random Fields for Spatial Data Modeling - A Primer for Scientists and Engineers (Hardcover, 1st ed. 2020)
Series: Advances in Geographic Information Science
Expected to ship within 9 - 17 working days
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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-Loeve 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.
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