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

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

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...

Full description

Saved in:
Bibliographic Details
Main Author: Hristopulos, Dionissios T.
Format: eBook
Language:English
Published: Dordrecht : Springer, 2020.
Series:Advances in geographic information science.
Subjects:
Random fields.
Spatial analysis (Statistics)
spatial analysis.
Random fields
Online Access:Click for online access
Table of Contents:
  • 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
  • Length Scales of Random Fields
  • Fractal Dimension
  • Long-Range Dependence
  • Intrinsic Random Fields
  • Fractional Brownian Motion
  • Classification of Random Fields
  • Gaussian Random Fields
  • Multivariate Normal Distribution
  • Field Integral Formulation
  • Useful Properties of Gaussian Random Fields
  • Perturbation Theory for Non-Gaussian Probability Densities
  • Non-stationary Covariance Functions
  • Further Reading
  • Random Fields based on Local Interactions
  • Spartan Spatial Random Fields
  • Two-point Functions and Realizations
  • Statistical and Geometric Properties
  • Bessel-Lommel Covariance Functions
  • Lattice Representations of Spartan Random Fields
  • Introduction to Gauss-Markov Random Fields
  • From Spartan Random Fields to Gauss-Markov Random Fields
  • Lattice Spectral Density
  • SSRF Lattice Moments
  • SSRF Inverse Covariance Operator on Lattices
  • Spartan Random Fields and Langevin Equations
  • Introduction to Stochastic Differential Equations
  • Classical Harmonic Oscillator
  • Stochastic Partial Differential Equations
  • Spartan Random Fields and Stochastic Partial Differential Equations
  • Covariance and Green's functions
  • Whittle-Matérn Stochastic Partial Differential Equation
  • Diversion in Time Series
  • Spatial Prediction Fundamentals
  • General Principles of Linear Prediction
  • Deterministic Interpolation
  • Stochastic Methods
  • Simple Kriging
  • Ordinary Kriging
  • Properties of the Kriging Predictor
  • Topics Related to the Application of Kriging
  • Evaluating Model Performance
  • More on Spatial Prediction
  • Linear Generalizations of Kriging
  • Nonlinear Extensions of Kriging
  • Connections with Gaussian Process Regression
  • Bayesian Kriging
  • Continuum Formulation of Linear Prediction
  • The "Local-Interaction" Approach
  • Big Spatial Data
  • Basic Concepts and Methods of Estimation
  • Estimator Properties
  • Estimating the Mean with Ordinary Kriging
  • Variogram Estimation
  • Maximum Likelihood Estimation
  • Cross Validation
  • More on Estimation
  • The Method of Normalized Correlations
  • The Method of Maximum Entropy
  • Stochastic Local Interactions
  • Measuring Ergodicity
  • Beyond the Gaussian Models
  • Trans-Gaussian Random Fields
  • Gaussian Anamorphosis
  • Tukey g-h Random Fields
  • Transformations based on Kappa Exponentials
  • Hermite Polynomials
  • Multivariate Student's t-distribution
  • Copula Models
  • The Replica Method
  • Binary Random Fields
  • The Indicator Random Field
  • Ising Model
  • Generalized Linear Models
  • Simulations
  • Introduction
  • Covariance Matrix Factorization
  • Spectral Simulation Methods
  • Fast-Fourier-Transform Simulation
  • Randomized Spectral Sampling
  • Conditional Simulation based on Polarization Method
  • Conditional Simulation based on Covariance Matrix Factorization
  • Monte Carlo Methods
  • Sequential Simulation of Random Fields
  • Simulated Annealing
  • Karhunen-Loève Expansion
  • Karhunen-Loève Expansion of Spartan Random Fields
  • Epilogue
  • A Jacobi's Transformation Theorems
  • B Tables of SSRF Properties
  • C Linear Algebra Facts
  • D Kolmogorov-Smirnov Test
  • Glossary
  • References
  • Index.

Similar Items