Parameter Estimation for Marked Gibbs Point Processes Through the Maximum Pseudo-likelihood Method

A general definition and derivation of the pseudo-likelihood function for marked Gibbs point processes are given. The maximum pseudo-likelihood method is illustrated by fitting some marked models to two data sets. In addition, a simulation study of statistical properties of the estimators is presented.

[1]  Y. Ogata,et al.  Estimation of Interaction Potentials of Marked Spatial Point Patterns Through the Maximum Likelihood Method , 1985 .

[2]  D. Stoyan.  Statistical inference for a Gibbs point process of mutually non-intersecting discs , 1989 .

[3]  D. Stoyan,et al.  Stochastic Geometry and Its Applications , 1989 .

[4]  A. Baddeley,et al.  Nearest-Neighbour Markov Point Processes and Random Sets , 1989 .

[5]  Valerie Isham,et al.  Multitype Markov point processes: some approximations , 1984, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[6]  Jens Ledet Jensen,et al.  Asymptotic Normality of Estimates in Spatial Point Processes , 1993 .

[7]  H. Künsch,et al.  On asymptotic normality of pseudo likelihood estimates for pairwise interaction processes , 1994, Annals of the Institute of Statistical Mathematics.

[8]  P. Diggle,et al.  On parameter estimation for pairwise interaction point processes , 1994 .

[9]  D. Stoyan,et al.  Stochastic Geometry and Its Applications , 1989 .

[10]  B. Ripley.  Modelling Spatial Patterns , 1977 .

[11]  S. Mase,et al.  Uniform LAN condition of planar Gibbsian point processes and optimality of maximum likelihood estimators of soft-core potential functions , 1992 .

[12]  J. Besag,et al.  Point process limits of lattice processes , 1982, Journal of Applied Probability.

[13]  B. Ripley.  Statistical inference for spatial processes , 1990 .

[14]  R. Takacs.  Estimator for the pair–potential of a gibbsian point process , 1986 .

[15]  Dietrich Stoyan,et al.  Marked Point Processes in Forest Statistics , 1992, Forest Science.

[16]  D. Stoyan,et al.  Statistical Analysis of Spatial Point Processes: A Soft-Core Model and Cross-Correlations of Marks , 1987 .

[17]  ON THE POSSIBLE FORM OF SIZE DISTRIBUTIONS FOR GIBBSIAN PROCESSES OF MUTUALLY NON-INTERSECTING BALLS , 1986 .

[18]  J. L. Jensen,et al.  Pseudolikelihood for Exponential Family Models of Spatial Point Processes , 1991 .

[19]  David Green,et al.  Statistical inference for spatial processes , 1990 .

[20]  Hans Zessin,et al.  Integral and Differential Characterizations of the GIBBS Process , 1979 .

[21]  A. Baddeley,et al.  Area-interaction point processes , 1993 .

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