Statistical reconstruction of random point patterns

A general reconstruction method is described which simulates point patterns possessing prescribed summary characteristics, which are free of explicit model conditions. The characteristics are for instance the intensity, the L-function, the spherical contact distribution function and the kth nearest neighbour distance distributions. The use of the statistical reconstruction method is demonstrated on both a theoretical and practical example.

[1]  Peter Winker,et al.  Applications of optimization heuristics to estimation and modelling problems , 2004, Comput. Stat. Data Anal..

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

[3]  Noel A Cressie,et al.  Statistics for Spatial Data. , 1992 .

[4]  Constantino Tsallis,et al.  Optimization by Simulated Annealing: Recent Progress , 1995 .

[5]  O. Barndorff-Nielsen,et al.  Stochastic Geometry , 1999 .

[6]  A. Baddeley,et al.  A cautionary example on the use of second-order methods for analyzing point patterns , 1984 .

[7]  Katja Schladitz,et al.  A third order point process characteristic , 1998, Advances in Applied Probability.

[8]  Arne Pommerening,et al.  Evaluating structural indices by reversing forest structural analysis , 2006 .

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

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

[11]  S. Torquato Random Heterogeneous Materials , 2002 .

[12]  A. Baddeley Spatial sampling and censoring , 2019, Stochastic Geometry.

[13]  B. Hambly Fractals, random shapes, and point fields , 1994 .

[14]  Mike Rees,et al.  5. Statistics for Spatial Data , 1993 .

[15]  Klaus Mecke,et al.  Simulating stochastic geometries: morphology of overlapping grains , 2002 .

[16]  Noel A Cressie,et al.  Statistics for Spatial Data, Revised Edition. , 1994 .

[17]  Peter J. Diggle,et al.  Modelling the Bivariate Spatial Distribution of Amacrine Cells , 2006 .