zbMATH — the first resource for mathematics

Statistical reconstruction of random point patterns. (English) Zbl 1157.62453
Summary: 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 \(k\)th nearest neighbour distance distributions. The use of the statistical reconstruction method is demonstrated on both a theoretical and practical example.

62H99 Multivariate analysis
62M99 Inference from stochastic processes
65C60 Computational problems in statistics (MSC2010)
Full Text: DOI
[1] Baddeley, A.J., Spatial sampling and censoring, (), 37-78
[2] Baddeley, A.J.; Silverman, B.W., A cautionary example on the use of second-order methods for analyzing point patterns, Biometrics, 40, 1089-1094, (1984)
[3] Brodatzki, U.; Mecke, K., Simulating stochastic geometries: morphology of overlapping grains, Comput. phys. comm., 147, 218-221, (2002) · Zbl 0999.60006
[4] Cressie, N.A.C., Statistics for spatial data, (1993), Wiley New York
[5] Diggle, P.J., Statistical analysis of spatial point patterns, (2003), Arnold Paris · Zbl 1021.62076
[6] Diggle, P.J., Eglen, S.J., Troy, J.B., 2005. Modelling the bivariate spatial distribution of amacrine cells. In: Baddeley, A.J., Gregori, P., Mateu, J., Stoica, R., Stoyan, D. (Eds.), Case Studies in Spatial Point Process Modeling. Lecture Notes in Statistics, Vol. 185, Springer, Berlin, pp. 215-234. · Zbl 05243463
[7] Kirkpatrick, S.; Gelatt, C.D.; Vecchi, M.P., Optimization by simulated annealing, Science, 220, 671-680, (1983) · Zbl 1225.90162
[8] Møller, J.; Waagepetersen, R.P., Statistical inference and simulation for spatial point processes, (2003), Chapman & Hall/CRC Boca Raton · Zbl 1039.62089
[9] Pommerening, A., 2006. Evaluating structural indices by reversing forest structural analysis. Forest Ecology and Management (in print).
[10] Pretzsch, H., Grundlagen der waldwachstumsforschung, (2002), Blackwell Berlin
[11] Schladitz, K.; Baddeley, A.J., A third order point process characteristic, Scand. J. statist., 27, 657-671, (2000) · Zbl 0962.62091
[12] Stoyan, D.; Stoyan, H., Fractals, random shapes and point fields, (1994), Wiley Chichester · Zbl 0828.62085
[13] Stoyan, D.; Kendall, W.S.; Mecke, J., Stochastic geometry and its applications, (1995), Wiley Chichester · Zbl 0838.60002
[14] Torquato, S., Random heterogeneous materials, (2001), Springer New York
[15] Tscheschel, A., 2001. Reconstruction of random porous media. Diploma dissertation, TU Bergakademie Freiberg, Germany.
[16] von Gadow, K., Hui, G.Y., 2002. Characterizing forest spatial structure and diversity. In: Björk, L. (Ed.), Sustainable Forestry in Temperate Regions. Proceedings of the SUFOR International Workshop, Lund University, pp. 20-30.
[17] Winker, P.; Gilli, M., Applications of optimization heuristics to estimation and modelling problems, Comput. statist. data anal., 47, 211-223, (2004) · Zbl 1429.62034
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.