Multi-dimensional Point Process Models in R

A software package for fitting and assessing multidimensional point process models using the R statistical computing environment is described. Methods of residual analysis based on random thinning are discussed and implemented. Features of the software are demonstrated using data on wildfire occurrences in Los Angeles County, California and earthquake occurrences in Northern California.

[1]  R. Peng,et al.  Multi-dimensional Point Process Models for Evaluating a Wildfire Hazard Index , 2003 .

[2]  Frederic Paik Schoenberg,et al.  Transforming Spatial Point Processes into Poisson Processes , 1999 .

[3]  A. Baddeley,et al.  Practical Maximum Pseudolikelihood for Spatial Point Patterns , 1998, Advances in Applied Probability.

[4]  G. Shedler,et al.  Simulation of Nonhomogeneous Poisson Processes by Thinning , 1979 .

[5]  Y. Ogata The asymptotic behaviour of maximum likelihood estimators for stationary point processes , 1978 .

[6]  Peter J. Diggle,et al.  SPLANCS: spatial point pattern analysis code in S-Plus , 1993 .

[7]  Stephen L. Rathbun,et al.  Asymptotic properties of the maximum likelihood estimator for spatio-temporal point processes , 1996 .

[8]  Ross Ihaka,et al.  Lexical Scope and Statistical Computing , 2000 .

[9]  Claude J. P. Bélisle Convergence theorems for a class of simulated annealing algorithms on ℝd , 1992 .

[10]  J. Chambers Programming with Data: A Guide to the S Language , 1998 .

[11]  Frederic Paik Schoenberg,et al.  Multidimensional Residual Analysis of Point Process Models for Earthquake Occurrences , 2003 .

[12]  Peter J. Diggle,et al.  Statistical analysis of spatial point patterns , 1983 .

[13]  R. Häggkvist,et al.  Second-order analysis of space-time clustering , 1995, Statistical methods in medical research.

[14]  Ross Ihaka,et al.  Gentleman R: R: A language for data analysis and graphics , 1996 .

[15]  Mark Berman,et al.  Approximating Point Process Likelihoods with Glim , 1992 .

[16]  D. Brillinger,et al.  Risk assessment: a forest fire example , 2003 .

[17]  B. Ripley The Second-Order Analysis of Stationary Point Processes , 1976 .

[18]  Daryl J. Daley,et al.  An Introduction to the Theory of Point Processes , 2013 .

[19]  Y. Ogata,et al.  Likelihood Analysis of Spatial Point Patterns , 1984 .

[20]  D. Vere-Jones Stochastic Models for Earthquake Occurrence , 1970 .

[21]  N. Cressie,et al.  Asymptotic Properties of Estimators for the Parameters of Spatial Inhomogeneous Poisson Point Processes , 1994, Advances in Applied Probability.

[22]  D. Vere-Jones,et al.  Some examples of statistical estimation applied to earthquake data , 1982 .