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Random Fields for Spatial Data Modeling

A Primer for Scientists and Engineers

  • Dionissios T. Hristopulos
Textbook
  • 1.7k Downloads

Part of the Advances in Geographic Information Science book series (AGIS)

Table of contents

  1. Front Matter
    Pages i-xxx
  2. Dionissios T. Hristopulos
    Pages 1-40
  3. Dionissios T. Hristopulos
    Pages 41-81
  4. Dionissios T. Hristopulos
    Pages 83-125
  5. Dionissios T. Hristopulos
    Pages 127-171
  6. Dionissios T. Hristopulos
    Pages 173-244
  7. Dionissios T. Hristopulos
    Pages 245-307
  8. Dionissios T. Hristopulos
    Pages 309-363
  9. Dionissios T. Hristopulos
    Pages 365-392
  10. Dionissios T. Hristopulos
    Pages 393-432
  11. Dionissios T. Hristopulos
    Pages 433-484
  12. Dionissios T. Hristopulos
    Pages 485-515
  13. Dionissios T. Hristopulos
    Pages 517-550
  14. Dionissios T. Hristopulos
    Pages 551-589
  15. Dionissios T. Hristopulos
    Pages 591-643
  16. Dionissios T. Hristopulos
    Pages 645-688
  17. Dionissios T. Hristopulos
    Pages 689-784
  18. Dionissios T. Hristopulos
    Pages 785-788
  19. Back Matter
    Pages 789-867

About this book

Introduction

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.

Keywords

Conditional Simulation Gaussian Statistical Field Theory Local Interaction Models Random Fields Spatial Analysis of Natural Systems Spatial Data Modelling Spatial Random Field Theory Spatial Statistics Stochastics Differential Equations

Authors and affiliations

  • Dionissios T. Hristopulos
    • 1
  1. 1.Technical University of CreteChaniaGreece

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-024-1918-4
  • Copyright Information Springer Nature B.V. 2020
  • Publisher Name Springer, Dordrecht
  • eBook Packages Earth and Environmental Science
  • Print ISBN 978-94-024-1916-0
  • Online ISBN 978-94-024-1918-4
  • Series Print ISSN 1867-2434
  • Series Online ISSN 1867-2442
  • Buy this book on publisher's site