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Volumn 42, Issue 3, 2000, Pages 283-322

Practical maximum pseudolikelihood for spatial point patterns

Author keywords

Area interaction process; Berman Turner device; Dirichlet tessellation; Edge effects; Generalized additive models; Generalized linear models; Gibbs point processes; GLIM; Hard core process; Inhomogeneous point process; Marked point processes

Indexed keywords


EID: 0005459531     PISSN: 13691473     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-842X.00128     Document Type: Article
Times cited : (330)

References (66)
  • 2
    • 0002867127 scopus 로고    scopus 로고
    • Spatial sampling and censoring
    • eds O.E. Barndorff-Nielsen, W.S. Kendall & M.N.M. van Lieshout, Chapter 2. London: Chapman & Hall
    • BADDELEY, A.J. (1998). Spatial sampling and censoring. In Stochastic Geometry: Likelihood and Computation, eds O.E. Barndorff-Nielsen, W.S. Kendall & M.N.M. van Lieshout, Chapter 2. London: Chapman & Hall.
    • (1998) Stochastic Geometry: Likelihood and Computation
    • Baddeley, A.J.1
  • 3
    • 0002826444 scopus 로고
    • Nearest-neighbour Markov point processes and random sets
    • BADDELEY, A.J. & MØLLER, J. (1989). Nearest-neighbour Markov point processes and random sets. Internat. Statist. Rev. 57, 89-121.
    • (1989) Internat. Statist. Rev. , vol.57 , pp. 89-121
    • Baddeley, A.J.1    Møller, J.2
  • 6
    • 0002807714 scopus 로고
    • Testing for spatial association between a point process and another stochastic process
    • BERMAN, M. (1986). Testing for spatial association between a point process and another stochastic process. Appl. Statist. 35, 54-62.
    • (1986) Appl. Statist. , vol.35 , pp. 54-62
    • Berman, M.1
  • 7
    • 0002733195 scopus 로고
    • Approximating point process likelihoods with GLIM
    • BERMAN, M. & TURNER, T.R. (1992). Approximating point process likelihoods with GLIM. Appl. Statist. 41, 31-38.
    • (1992) Appl. Statist. , vol.41 , pp. 31-38
    • Berman, M.1    Turner, T.R.2
  • 8
    • 0000582521 scopus 로고
    • Statistical analysis of non-lattice data
    • BESAG, J. (1975). Statistical analysis of non-lattice data. The Statistician 24, 179-195.
    • (1975) The Statistician , vol.24 , pp. 179-195
    • Besag, J.1
  • 9
    • 0002673581 scopus 로고
    • Some methods of statistical analysis for spatial data
    • BESAG, J. (1977). Some methods of statistical analysis for spatial data. Bull. Internat. Statist. Inst. 47, 77-92.
    • (1977) Bull. Internat. Statist. Inst. , vol.47 , pp. 77-92
    • Besag, J.1
  • 10
    • 0000163477 scopus 로고
    • Point process limits of lattice processes
    • BESAG, J., MILNE, R. & ZACHARY, S. (1982). Point process limits of lattice processes. J. Appl. Probab. 19, 210-216.
    • (1982) J. Appl. Probab. , vol.19 , pp. 210-216
    • Besag, J.1    Milne, R.2    Zachary, S.3
  • 14
    • 0002972364 scopus 로고
    • Spatial clustering for inhomogeneous populations
    • CUZICK, J. & EDWARDS, R. (1990). Spatial clustering for inhomogeneous populations. J. Roy. Statist. Soc. Ser. B 52, 73-104.
    • (1990) J. Roy. Statist. Soc. Ser. B , vol.52 , pp. 73-104
    • Cuzick, J.1    Edwards, R.2
  • 17
    • 0000423415 scopus 로고
    • Estimation of parameterized pair potentials of marked and non-marked Gibbsian point processes
    • FIKSEL, T. (1984). Estimation of parameterized pair potentials of marked and non-marked Gibbsian point processes. Elektron. Informationsverarb. Kybernet. 20, 270-278.
    • (1984) Elektron. Informationsverarb. Kybernet. , vol.20 , pp. 270-278
    • Fiksel, T.1
  • 18
    • 0002985683 scopus 로고
    • Estimation of interaction potentials of Gibbsian point processes
    • FIKSEL, T. (1988). Estimation of interaction potentials of Gibbsian point processes. Statistics 19, 77-86.
    • (1988) Statistics , vol.19 , pp. 77-86
    • Fiksel, T.1
  • 19
    • 0343576885 scopus 로고    scopus 로고
    • Marked point processes in the plane I - A survey with applications to spatial modeling of communication networks
    • FREY, A. & SCHMIDT, V. (1998). Marked point processes in the plane I - a survey with applications to spatial modeling of communication networks. Adv. in Performance Analysis 1, 65-110.
    • (1998) Adv. in Performance Analysis , vol.1 , pp. 65-110
    • Frey, A.1    Schmidt, V.2
  • 20
    • 0002218961 scopus 로고    scopus 로고
    • Likelihood inference for spatial point processes
    • eds O.E. Barndorff-Nielsen, W.S. Kendall & M.N.M. van Lieshout, number 80 in Monographs on Statistics and Applied Probability, Chapter 3. CRC, Boca Raton: Chapman & Hall
    • GEYER, C.J. (1999). Likelihood inference for spatial point processes. In Stochastic Geometry: Likelihood and Computation, eds O.E. Barndorff-Nielsen, W.S. Kendall & M.N.M. van Lieshout, number 80 in Monographs on Statistics and Applied Probability, Chapter 3. CRC, Boca Raton: Chapman & Hall.
    • (1999) Stochastic Geometry: Likelihood and Computation
    • Geyer, C.J.1
  • 21
    • 0001309227 scopus 로고
    • Simulation procedures and likelihood inference for spatial point processes
    • GEYER, C.J. & MØLLER, J. (1994). Simulation procedures and likelihood inference for spatial point processes. Scand. J. Statist. 21, 359-373.
    • (1994) Scand. J. Statist. , vol.21 , pp. 359-373
    • Geyer, C.J.1    Møller, J.2
  • 22
    • 0011345042 scopus 로고
    • Bemerkungen zu einer Arbeit von O.K
    • GLÖTZL, E. (1980a). Bemerkungen zu einer Arbeit von O.K. Kozlov. Math. Nachr. 94, 277-289.
    • (1980) Kozlov. Math. Nachr. , vol.94 , pp. 277-289
    • Glötzl, E.1
  • 23
    • 0011295476 scopus 로고
    • Lokale Energien und Potentiale für Punktprozessen
    • GLÖTZL, E. (1980b). Lokale Energien und Potentiale für Punktprozessen. Math. Nachr. 96, 195-206.
    • (1980) Math. Nachr. , vol.96 , pp. 195-206
    • Glötzl, E.1
  • 24
    • 0040304544 scopus 로고    scopus 로고
    • Parameter estimation for marked Gibbs point processes through the maximum pseudolikelihood method
    • GOULARD, M., SÄRKKÄ, A. & GRABARNIK P. (1996). Parameter estimation for marked Gibbs point processes through the maximum pseudolikelihood method. Scand. J. Statist. 23, 365-379.
    • (1996) Scand. J. Statist. , vol.23 , pp. 365-379
    • Goulard, M.1    Särkkä, A.2    Grabarnik, P.3
  • 25
    • 0342581605 scopus 로고
    • Relationships between the multinomial and Poisson models of stochastic processes, and between the canonical and grand canonical ensembles in statistical mechanics, with illustrations and Monte Carlo methods for the penetrable sphere model of liquid-vapour equilibrium
    • HAMMERSLEY, J.M., LEWIS, J.W.E. & ROWLINSON, J.S. (1975). Relationships between the multinomial and Poisson models of stochastic processes, and between the canonical and grand canonical ensembles in statistical mechanics, with illustrations and Monte Carlo methods for the penetrable sphere model of liquid-vapour equilibrium. Sankhyā Ser. A 37, 457-491.
    • (1975) Sankhyā Ser. A , vol.37 , pp. 457-491
    • Hammersley, J.M.1    Lewis, J.W.E.2    Rowlinson, J.S.3
  • 26
    • 0001620770 scopus 로고
    • A bivariate spatial point pattern of ants' nests
    • HARKNESS, R.D. & ISHAM, V. (1983). A bivariate spatial point pattern of ants' nests. Appl. Statist. 32, 293-303.
    • (1983) Appl. Statist. , vol.32 , pp. 293-303
    • Harkness, R.D.1    Isham, V.2
  • 28
    • 0021758354 scopus 로고
    • Multitype Markov point processes: Some approximations
    • ISHAM, V.S. (1984). Multitype Markov point processes: some approximations. Proc. Roy. Soc. London Ser. A 39, 39-53.
    • (1984) Proc. Roy. Soc. London Ser. A , vol.39 , pp. 39-53
    • Isham, V.S.1
  • 29
    • 0000716774 scopus 로고
    • On asymptotic normality of pseudo likelihood estimates for pairwise interaction processes
    • JENSEN, J.L. & KÜNSCH, H.R. (1994). On asymptotic normality of pseudo likelihood estimates for pairwise interaction processes. Ann. Inst. Statist. Math. 46, 475-486.
    • (1994) Ann. Inst. Statist. Math. , vol.46 , pp. 475-486
    • Jensen, J.L.1    Künsch, H.R.2
  • 30
    • 0000849716 scopus 로고
    • Pseudolikelihood for exponential family models of spatial point processes
    • JENSEN, J.L. & MØLLER, J. (1991). Pseudolikelihood for exponential family models of spatial point processes. Ann. Appl. Probab. 1, 445-461.
    • (1991) Ann. Appl. Probab. , vol.1 , pp. 445-461
    • Jensen, J.L.1    Møller, J.2
  • 31
    • 0004212801 scopus 로고
    • Berlin/New York: Akademie Verlag/Academic Press
    • KALLENBERG, O. (1983). Random Measures. 3rd edn. Berlin/New York: Akademie Verlag/Academic Press.
    • (1983) Random Measures. 3rd Edn.
    • Kallenberg, O.1
  • 32
    • 0001403399 scopus 로고
    • An informal guide to the theory of conditioning in point processes
    • KALLENBERG, O. (1984). An informal guide to the theory of conditioning in point processes. Internat. Statist. Rev. 52, 151-164.
    • (1984) Internat. Statist. Rev. , vol.52 , pp. 151-164
    • Kallenberg, O.1
  • 33
    • 0017154989 scopus 로고
    • On Strauss's model for clustering
    • KELLY, F.P. & RIPLEY, B.D. (1976). On Strauss's model for clustering. Biometrika 63, 357-360.
    • (1976) Biometrika , vol.63 , pp. 357-360
    • Kelly, F.P.1    Ripley, B.D.2
  • 35
    • 0011340959 scopus 로고
    • Gibbsian description of point random fields
    • KOZLOV, O.K. (1976). Gibbsian description of point random fields. Theory Probab. Appl. 21, 339-355.
    • (1976) Theory Probab. Appl. , vol.21 , pp. 339-355
    • Kozlov, O.K.1
  • 37
    • 13344283926 scopus 로고
    • Fitting parametric counting processes by using linear models
    • LINDSEY, J.K. ( 1995). Fitting parametric counting processes by using linear models. Appl. Statist. 44, 201-212.
    • (1995) Appl. Statist. , vol.44 , pp. 201-212
    • Lindsey, J.K.1
  • 38
    • 0040753717 scopus 로고    scopus 로고
    • Fitting bivariate intensity functions, with an application to modelling delays in reporting acquired immune deficiency syndrome
    • LINDSEY, J.K. (1996). Fitting bivariate intensity functions, with an application to modelling delays in reporting acquired immune deficiency syndrome. J. Roy. Statist. Soc. Ser. A, 159, 125-131.
    • (1996) J. Roy. Statist. Soc. Ser. A , vol.159 , pp. 125-131
    • Lindsey, J.K.1
  • 39
    • 38249013496 scopus 로고
    • Fitting and comparing probability distributions with log linear models
    • LINDSEY, J.K. & MERSCH, G. (1992). Fitting and comparing probability distributions with log linear models. Comput. Statist. Data Anal. 13, 373-384.
    • (1992) Comput. Statist. Data Anal. , vol.13 , pp. 373-384
    • Lindsey, J.K.1    Mersch, G.2
  • 41
    • 0002755026 scopus 로고
    • Stochastic approximation for the MLE of a spatial point process
    • MOYEED, R.A. & BADDELEY, A.J. (1991). Stochastic approximation for the MLE of a spatial point process. Scand. J. Statist. 18, 39-50.
    • (1991) Scand. J. Statist. , vol.18 , pp. 39-50
    • Moyeed, R.A.1    Baddeley, A.J.2
  • 43
    • 0011366715 scopus 로고    scopus 로고
    • Research Report 2, Laboratory for Computational Stochastics. Department of Mathematical Sciences, University of Aarhus
    • NIELSEN, L.S. & JENSEN, E.B.V. (1998). Inhomogeneous Markov Point Processes by Transformation. Research Report 2, Laboratory for Computational Stochastics. Department of Mathematical Sciences, University of Aarhus.
    • (1998) Inhomogeneous Markov Point Processes by Transformation
    • Nielsen, L.S.1    Jensen, E.B.V.2
  • 44
    • 0002399265 scopus 로고
    • Forest vegetation, particularly pine stems in the vicinity of Choshi - Coastal flora and vegetation in Choshi, Chiba prefecture, IV
    • Chiba University
    • NUMATA, M. (1964). Forest vegetation, particularly pine stems in the vicinity of Choshi - coastal flora and vegetation in Choshi, Chiba prefecture, IV. (In Japanese) Bulletin of the Choshi Marine Laboratory 6, 27-37. Chiba University.
    • (1964) (In Japanese) Bulletin of the Choshi Marine Laboratory , vol.6 , pp. 27-37
    • Numata, M.1
  • 45
    • 51249183003 scopus 로고
    • Estimation of interaction potentials of spatial point patterns through the maximum likelihood procedure
    • OGATA, Y. & TANEMURA, M. (1981). Estimation of interaction potentials of spatial point patterns through the maximum likelihood procedure. Ann. Inst. Statist. Math. 33, 315-338.
    • (1981) Ann. Inst. Statist. Math. , vol.33 , pp. 315-338
    • Ogata, Y.1    Tanemura, M.2
  • 46
    • 0000333882 scopus 로고
    • Likelihood analysis of spatial point patterns
    • OGATA, Y. & TANEMURA, M. (1984). Likelihood analysis of spatial point patterns. J. Roy. Statist. Soc. Ser. B 46, 496-518.
    • (1984) J. Roy. Statist. Soc. Ser. B , vol.46 , pp. 496-518
    • Ogata, Y.1    Tanemura, M.2
  • 47
    • 0022251657 scopus 로고
    • Estimation of interaction potentials of marked spatial point processes through the maximum likelihood method
    • OGATA, Y. & TANEMURA, M. (1985). Estimation of interaction potentials of marked spatial point processes through the maximum likelihood method. Biometrics 41, 421-433.
    • (1985) Biometrics , vol.41 , pp. 421-433
    • Ogata, Y.1    Tanemura, M.2
  • 48
    • 0001564783 scopus 로고
    • Likelihood estimation of interaction potentials and external fields of inhomogeneous spatial point patterns
    • eds I.S. Francis, B.J.F. Manly & F.C. Lam, Elsevier
    • OGATA, Y. & TANEMURA, M. (1986). Likelihood estimation of interaction potentials and external fields of inhomogeneous spatial point patterns. In Pacific Statistical Congress, eds I.S. Francis, B.J.F. Manly & F.C. Lam, pp. 150-154. Elsevier.
    • (1986) Pacific Statistical Congress , pp. 150-154
    • Ogata, Y.1    Tanemura, M.2
  • 51
    • 0004172223 scopus 로고
    • Berlin; Heidelberg; New York: Springer Verlag
    • PRESTON, C.J. (1976). Random Fields. Berlin; Heidelberg; New York: Springer Verlag.
    • (1976) Random Fields
    • Preston, C.J.1
  • 52
    • 0000135848 scopus 로고
    • Modelling spatial patterns
    • RIPLEY, B.D. (1977). Modelling spatial patterns (with discussion). J. Roy. Statist. Soc. Ser. B 39, 172-212.
    • (1977) J. Roy. Statist. Soc. Ser. B , vol.39 , pp. 172-212
    • Ripley, B.D.1
  • 55
    • 0010119274 scopus 로고
    • Gibbsian interaction models
    • ed. D.A. Griffiths, New York: Image
    • RIPLEY, B.D. (1989). Gibbsian interaction models. In Spatial Statistics: Past, Present and Future, ed. D.A. Griffiths, pp. 1-19. New York: Image.
    • (1989) Spatial Statistics: Past, Present and Future , pp. 1-19
    • Ripley, B.D.1
  • 56
    • 0008676424 scopus 로고
    • Penetrable sphere models of liquid-vapor equilibrium
    • ROWLINSON, J.S. (1980). Penetrable sphere models of liquid-vapor equilibrium. Adv. Chem. Phys. 41, 1-57.
    • (1980) Adv. Chem. Phys. , vol.41 , pp. 1-57
    • Rowlinson, J.S.1
  • 60
    • 0005856429 scopus 로고
    • A model for stand growth
    • INRA, Institut National de la Recherche Agronomique, Paris
    • STRAND, L. (1972). A model for stand growth. IUFRO Third Conference Advisory Group of Forest Statisticians. INRA, Institut National de la Recherche Agronomique, Paris, pp. 207-216.
    • (1972) IUFRO Third Conference Advisory Group of Forest Statisticians , pp. 207-216
    • Strand, L.1
  • 61
    • 0016689445 scopus 로고
    • A model for clustering
    • STRAUSS, D.J. (1975). A model for clustering. Biometrika 63, 467-475.
    • (1975) Biometrika , vol.63 , pp. 467-475
    • Strauss, D.J.1
  • 62
    • 0001287396 scopus 로고
    • Estimator for the pair potential of a Gibbsian point process
    • TAKACS, R. (1986). Estimator for the pair potential of a Gibbsian point process. Statistics 17, 429-433.
    • (1986) Statistics , vol.17 , pp. 429-433
    • Takacs, R.1
  • 63
    • 84981994045 scopus 로고
    • Interaction pair-potentials for a system of ants' nests
    • TAKACS, R. & FIKSEL, T. (1986). Interaction pair-potentials for a system of ants' nests. Biometrical J. 28, 1007-1013.
    • (1986) Biometrical J. , vol.28 , pp. 1007-1013
    • Takacs, R.1    Fiksel, T.2
  • 66
    • 36849104022 scopus 로고
    • New model for the study of liquid-vapor phase transitions
    • WIDOM, B. & ROWLINSON, J.S. (1970). New model for the study of liquid-vapor phase transitions. J. Chem. Phys. 52, 1670-1684.
    • (1970) J. Chem. Phys. , vol.52 , pp. 1670-1684
    • Widom, B.1    Rowlinson, J.S.2


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