Previous |  Up |  Next


MSC: 62H12, 62M05
Full entry | Fulltext not available (moving wall 24 months)      Feedback
Bayesian method; Monte Carlo Markov chain; Neyman-Scott point process; parameter estimation; shot-noise Cox process; Thomas process
The pure and modified Bayesian methods are applied to the estimation of parameters of the Neyman-Scott point process. Their performance is compared to the fast, simulation-free methods via extensive simulation study. Our modified Bayesian method is found to be on average 2.8 times more accurate than the fast methods in the relative mean square errors of the point estimates, where the average is taken over all studied cases. The pure Bayesian method is found to be approximately as good as the fast methods. These methods are computationally affordable today.
[1] Baddeley, A., Turner, R.: An R Package for analyzing spatial point patterns. J. Stat. Software 12 (2005), 1-42. DOI 10.18637/jss.v012.i06
[2] Diggle, P. J., Gratton, R. J.: Monte Carlo methods of inference for implicit statistical models. J. R. Stat. Soc., Ser. B 46 (1984), 193-227. MR 0781880 | Zbl 0561.62035
[3] Dvořák, J., Prokešová, M.: Moment estimation methods for stationary spatial Cox processes---a simulation study. Preprint (2011),{dvorak/CoxEstimation/CoxEstimation_SimulationStudy.pdf} MR 3086866
[4] Dvořák, J., Prokešová, M.: Moment estimation methods for stationary spatial Cox processes---a comparison. Kybernetika 48 (2012), 1007-1026. MR 3086866 | Zbl 1297.62201
[5] Guan, Y.: A composite likelihood approach in fitting spatial point process models. J. Am. Stat. Assoc. 101 (2006), 1502-1512. DOI 10.1198/016214506000000500 | MR 2279475 | Zbl 1171.62348
[6] Guttorp, P., Thorarinsdottir, T. L.: Bayesian inference for non-Markovian point processes. J. M. Montero, M. Schlather Advances and Challenges in Space-Time Modelling of Natural Events Lecture Notes in Statistics 207 Springer, Berlin 79-102 (2012).
[7] Illian, J., Penttinen, A., Stoyan, H., Stoyan, D.: Statistical Analysis and Modelling of Spatial Point Patterns. Statistics in Practice. John Wiley & Sons, Chichester (2008). MR 2384630
[8] Møller, J., Waagepetersen, R. P.: Statistical Inference and Simulation for Spatial Point Processes. Monographs on Statistics and Applied Probability 100 Chapman and Hall/CRC, Boca Raton (2004). MR 2004226 | Zbl 1044.62101
[9] Møller, J., Waagepetersen, R. P.: Modern statistics for spatial point processes. Scand. J. Stat. 34 (2007), 643-684. MR 2392447 | Zbl 1157.62067
[10] Mrkvička, T.: Distinguishing different types of inhomogeneity in Neyman-Scott point processes. Methodol. Comput. Appl. Probab. 16 (2014), 385-395. DOI 10.1007/s11009-013-9365-4 | MR 3199053 | Zbl 1305.62337
[11] Mrkvička, T., Muška, M., Kubečka, J.: Two step estimation for Neyman-Scott point process with inhomogeneous cluster centers. Stat. Comput. 24 (2014), 91-100. DOI 10.1007/s11222-012-9355-3 | MR 3147700 | Zbl 1325.62077
[12] Neyman, J., Scott, E. L.: A theory for the spatial distribution of galaxies. Astrophys. J. 116 (1952), 144-163. DOI 10.1086/145599 | MR 0053640
[13] Stoyan, D., Kendall, W. S., Mecke, J.: Stochastic Geometry and Its Applications. Wiley Series in Probability and Mathematical Statistics John Wiley & Sons, Chichester (1995). MR 0895588 | Zbl 0838.60002
[14] Tanaka, U., Ogata, Y., Stoyan, D.: Parameter estimation and model selection for Neyman-Scott point processes. Biom. J. 50 (2008), 43-57. DOI 10.1002/bimj.200610339 | MR 2414637
[15] Research, Wolfram, Inc.: Mathematica, Version 8.0. Champaign, IL (2010).
Partner of
EuDML logo