Spatial Process Generation

The generation of random spatial data on a computer is an important tool for understanding the behavior of spatial processes. In this paper we describe how to generate realizations from the main types of spatial processes, including Gaussian and Markov random fields, point processes, spatial Wiener processes, and Levy fields. Concrete MATLAB code is provided.

[1]  Michael W. Mislove,et al.  AN INTRODUCTION TO THE THEORY OF , 1982 .

[2]  L. Breuer Introduction to Stochastic Processes , 2022, Statistical Methods for Climate Scientists.

[3]  Wang,et al.  Nonuniversal critical dynamics in Monte Carlo simulations. , 1987, Physical review letters.

[4]  J. Neyman,et al.  Statistical Approach to Problems of Cosmology , 1958 .

[5]  C. Geyer,et al.  Simulation Procedures and Likelihood Inference for Spatial Point Processes , 1994 .

[6]  Adrian Baddeley,et al.  Spatial Point Processes and their Applications , 2007 .

[7]  David J. Strauss Analysing binary lattice data with the nearest-neighbor property , 1975 .

[8]  A. T. A. Wood,et al.  Simulation of stationary Gaussian vector fields , 1999, Stat. Comput..

[9]  Carolyn R. Bertozzi,et al.  Methods and Applications , 2009 .

[10]  Jeff Dean,et al.  Time Series , 2009, Encyclopedia of Database Systems.

[11]  佐藤 健一 Lévy processes and infinitely divisible distributions , 2013 .

[12]  Jürgen Symanzik,et al.  Statistical Analysis of Spatial Point Patterns , 2005, Technometrics.

[13]  C. R. Dietrich,et al.  Fast and Exact Simulation of Stationary Gaussian Processes through Circulant Embedding of the Covariance Matrix , 1997, SIAM J. Sci. Comput..

[14]  Dirk P. Kroese,et al.  Handbook of Monte Carlo Methods , 2011 .

[15]  Hong Qian,et al.  On two-dimensional fractional Brownian motion and fractional Brownian random field. , 1998, Journal of physics A: Mathematical and general.

[16]  R. Cowan An introduction to the theory of point processes , 1978 .

[17]  B. Mandelbrot,et al.  Fractional Brownian Motions, Fractional Noises and Applications , 1968 .

[18]  F. Kelly,et al.  A note on Strauss's model for clustering , 1976 .

[19]  A. Wood,et al.  Simulation of Stationary Gaussian Processes in [0, 1] d , 1994 .

[20]  Volker Schmidt,et al.  Efficient simulation of charge transport in deep-trap media , 2012, Proceedings Title: Proceedings of the 2012 Winter Simulation Conference (WSC).

[21]  A. Brix Generalized Gamma measures and shot-noise Cox processes , 1999, Advances in Applied Probability.

[22]  A. Zinober Matrices: Methods and Applications , 1992 .

[23]  Robert Tibshirani,et al.  An Introduction to the Bootstrap , 1994 .

[24]  J. Møller,et al.  Statistical Inference and Simulation for Spatial Point Processes , 2003 .

[25]  Hoon Kim,et al.  Monte Carlo Statistical Methods , 2000, Technometrics.

[26]  Dirk P. Kroese,et al.  Graph-based simulated annealing: a hybrid approach to stochastic modeling of complex microstructures , 2013 .

[27]  T. Gneiting,et al.  Fast and Exact Simulation of Large Gaussian Lattice Systems in ℝ2: Exploring the Limits , 2006 .

[28]  Robert H. Halstead,et al.  Matrix Computations , 2011, Encyclopedia of Parallel Computing.

[29]  D. Cox Some Statistical Methods Connected with Series of Events , 1955 .

[30]  Hans-Peter Scheffler,et al.  Simulation of Infinitely Divisible Random Fields , 2009, Commun. Stat. Simul. Comput..

[31]  P. Green Reversible jump Markov chain Monte Carlo computation and Bayesian model determination , 1995 .

[32]  Leonhard Held,et al.  Gaussian Markov Random Fields: Theory and Applications , 2005 .

[33]  Jorge Mateu,et al.  Case Studies in Spatial Point Process Modeling , 2006 .