Estimating Second-Order Characteristics of Inhomogeneous Spatio-Temporal Point Processes

Methodology and Computing in Applied Probability - Tập 16 Số 2 - Trang 411-431 - 2014
Edith Gabriel1
1Avignon University, Avignon, France

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Allard D, Brix A, Chadoeuf J (2001) Testing local independence between two point processes. Biometrics 57:508–517

Arbia G, Espa G, Giuliani D, Mazzitelli A (2012) Clusters of firms in an inhomogeneous space: the high-tech industries in milan. Econ Model 29(1):3–11

Baddeley A (1999) Spatial sampling and censoring. In: Barndorff-Nielsen O, Kendall W, van Lieshout M (eds) Stochastic geometry: likelihood and computation. Chapman and Hall/CRC, London, pp 449–461

Baddeley A, Turner R (2000) Practical maximum pseudolikelihood for spatial point patterns. Aust NZ J Stat 42:283–322

Baddeley A, Moyeed R, Howard C, Boyde A (1993) Analysis of a three-dimensional point pattern with replication. Appl Stat 42(4):641–668

Baddeley A, Møller J, Waagepetersen R (2000) Non- and semi-parametric estimation of interaction in inhomogeneous point patterns. Stat Neerl 54(3):329–350

Berman M, Diggle P (1989) Estimating weighted integrals of the second-order intensity of a spatial point process. J Roy Stat Soc B 51:81–92

Berman M, Turner T (1992) Approximating point process likelihoods with GLIM. Appl Stat 41:31–38

Brix A, Senoussi R, Couteron P, Chadoeuf J (2001) Assessing goodness of fit of spatially inhomogeneous Poisson processes. Biometrika 88(2):487–497

Cressie N (1993) Statistics for spatial data, revised edn. Wiley, New York

Cressie N, Wikle C (2011) Statistics for spatio-temporal data, 1st edn. Wiley, New York

Cronie O, Särkka A (2011) Some edge correction methods for marked spatio-temporal point process models. Comput Stat Data An 55(7):2209–2220

Daley D, Vere-Jones D (2003) An introduction to the theory of point processes, vol I: Elementary theory and methods, 2nd edn. Springer, New York

Diggle P (1979) On parameter estimation and goodness-of-fit testing for spatial point patterns. Biometrics 35:87–101

Diggle P (1985) A kernel method for smoothing point process data. Appl Stat 34(2):138–147

Diggle P (2003) Statistical analysis of spatial point patterns, 2nd edn. Edward Arnold, London

Diggle P (2006) Spatio-temporal point processes: methods and applications. In: Finkenstadt B, Held L, Isham V (eds) Statistical methods for spatio-temporal systems, monographs on statistics and applied probability. Chapman and Hall/CRC, London, pp 1–45

Diggle P, Gabriel E (2010) Spatio-temporal point processes. In: Gelfand A, Diggle P, Fuentes M, Guttorp P (eds) Handbook of spatial statistics. Chapman and Hall/CRC, London, pp 449–461

Diggle P, Lange N, Benes F (1991) Analysis of variance for replicated spatial point patterns in clinical neuroanatomy. J Am Stat Assoc 86:618–625

Diggle P, Chetwynd A, Häggkvist R, Gooding S (1995) Second-order analysis of space-time clustering. Stat Methods Med Res 4:124–136

Diggle P, Gómez-Rubio V, Brown P, Chetwynd A, Gooding S (2007) Second-order analysis of inhomogeneous spatial point processes using case-control data. Biometrics 63(2):550–557

Doguwa S (1990) On edge-corrected kernel-based pair-correlation function estimators for point processes. Biom J 32:95–106

Gabriel E (2013) Estimating second-order characteristics of inhomogeneous spatio-temporal point processes: influence of edge correction methods and intensity estimates. ArXiv: e-prints1304.7178

Gabriel E, Diggle P (2009) Second-order analysis of inhomogeneous spatio-temporal point process data. Stat Neerl 63(1):43–51

Gabriel E, Wilson D, Leatherbarrow H, Cheesbrough J, Gee S, Bolton E, Fox A, Fearnhead P, Hart A, Diggle P (2010) Spatio-temporal epidemiology of campylobacter jejuni enteritis, in an area of northwest england, 2000–2002. Epidemiol Infect 138:1384–1390

Gabriel E, Rowlingson B, Diggle P (2013) stpp: an R package for plotting, simulating and analysing spatio-temporal point patterns. J Stat Softw 53(2):1:29

Goreaud F, Pélissier R (1999) On explicit formulas of edge effect correction for Ripley’s K-function. J Veg Sci 10(3):433–438

Guan Y, Sherman M, Calvin J (2006) Assessing isotropy for spatial point processes. Biometrics 62:119–125

Haase P (1995) Spatial pattern analysis in ecology based on Ripley’s K-function: introduction and methods of edge correction. J Veg Sci 6:575–582

Illian J, Penttinen A, Stoyan H, Stoyan D (2008) Statistical analysis and modelling of spatial point patterns. Wiley

Jafari-Mamaghani M, Andersson M, Krieger P (2010) Spatial point pattern analysis of neurons using Ripley’s K-function in 3D. Front Neuroinform 4:1–10

Law R, Illian J, Burslem D, Gratzer G, Gunatilleke C, Gunatilleke I (2009) Ecological information from spatial patterns of plants: insights from point process theory. J Ecol 97(4):616–628

Li F, Zhang L (2007) Comparison of point pattern analysis methods for classifying the spatial distributions of spurce-fir stands in the north-east usa. Forestry 80(3):337–349

Liu D, Kelly M, Gong P, Guo Q (2007) Characterizing spatial-temporal tree mortality patterns associated with a new forest disease. For Ecol Manag 253:220–231

Møller J (2003) Shot-noise Cox processes. Adv Appl Probab 35(3):614–640

Møller J, Díaz-Avalos C (2010) Structured spatio-temporal shot-noise Cox point process models, with a view to modelling forest fires. Scan J Stat 37(1):2–25

Møller J, Ghorbani M (2012) Aspects of second-order analysis of structured inhomogeneous spatio-temporal point processes. Stat Neerl 66:472–491

Møller J, Toftager H (2012) Geometric anisotropic spatial point pattern analysis and Cox processes. Tech. Rep. R-2012-01, Department of Mathematical Sciences, Aalborg University

Møller J, Waagepetersen R (2003) Statistical inference and simulation for spatial point processes. Monographs on statistics and applied probability. Chapman and Hall/CRC, London

Mrkvička T, Muška M, Kubečka J (2012) Two step estimation for Neyman-Scott point process with inhomogeneous cluster centers. Stat Comp. doi: 10.1007/s11222-012-9355-3

Ohser J (1983) On estimators for the reduced second moment measure of point processes. Math Oper Stat 14:63–71

Pommerening A, Stoyan D (2006) Edge-correction needs in estimating indices of spatial forest structure. Can J For Res 36:1723–1739

Prokešová M (2010) Inhomogeneity in spatial Cox point processes—location dependent thinning is not the only option. Image Anal Stereol 29:133–141

R Development Core Team (2012) R: a language and environment for statistical computing. R foundation for statistical computing. Vienna Austria. http://www.r-project.org

Ripley B (1977) Modelling spatial patterns (with discussion). J Roy Stat Soc B 39:172–212

Ripley B (1988) Statistical inference for spatial processes. Cambrige University Press, Cambridge

Silverman B (1986) Density estimation for statistics and data analysis. Chapman and Hall/CRC, London

Stoyan D, Stoyan H (1994) Fractals, random shapes and point fields: methods of geometrical statistics. Wiley

Vere-Jones D (2009) Some models and procedures for space-time point processes. Env Ecol Stat 16(2):173–195

Yamada I, Rogerson P (2003) An empirical comparison of edge effect correction methods applied to K-function analysis. Geogr Anal 35(2):97–109

Zhuang J, Ogata Y, Jones D (2002) Stochastic declustering of space-time earthquake occurrences. J Am Stat Assoc 97(458):369–380