Inference for Clustered Inhomogeneous Spatial Point Processes
We propose a method to test for significant differences in the levels of clustering between two spatial point processes (cases and controls) while taking into account differences in their first-order intensities. The key advance on earlier methods is that the controls are not assumed to be a Poisson...
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| Vydáno v: | Biometrics Ročník 65; číslo 2; s. 423 - 430 |
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| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
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Malden, USA
Blackwell Publishing Inc
01.06.2009
Wiley-Blackwell Publishing Blackwell Publishing Ltd |
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| ISSN: | 0006-341X, 1541-0420, 1541-0420 |
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| Abstract | We propose a method to test for significant differences in the levels of clustering between two spatial point processes (cases and controls) while taking into account differences in their first-order intensities. The key advance on earlier methods is that the controls are not assumed to be a Poisson process. Inference and diagnostics are based around the inhomogeneous K-function with confidence envelopes obtained from either resampling events in a nonparametric bootstrap approach, or simulating new events as in a parametric bootstrap. Methods developed are demonstrated using the locations of adult and juvenile trees in a tropical forest. A simulation study briefly examines the accuracy and power of the inferential procedures. |
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| AbstractList | We propose a method to test for significant differences in the levels of clustering between two spatial point processes (cases and controls) while taking into account differences in their first-order intensities. The key advance on earlier methods is that the controls are not assumed to be a Poisson process. Inference and diagnostics are based around the inhomogeneous K-function with confidence envelopes obtained from either resampling events in a nonparametric bootstrap approach, or simulating new events as in a parametric bootstrap. Methods developed are demonstrated using the locations of adult and juvenile trees in a tropical forest. A simulation study briefly examines the accuracy and power of the inferential procedures. Summary We propose a method to test for significant differences in the levels of clustering between two spatial point processes (cases and controls) while taking into account differences in their first‐order intensities. The key advance on earlier methods is that the controls are not assumed to be a Poisson process. Inference and diagnostics are based around the inhomogeneous K‐function with confidence envelopes obtained from either resampling events in a nonparametric bootstrap approach, or simulating new events as in a parametric bootstrap. Methods developed are demonstrated using the locations of adult and juvenile trees in a tropical forest. A simulation study briefly examines the accuracy and power of the inferential procedures. Summary We propose a method to test for significant differences in the levels of clustering between two spatial point processes (cases and controls) while taking into account differences in their first‐order intensities. The key advance on earlier methods is that the controls are not assumed to be a Poisson process. Inference and diagnostics are based around the inhomogeneous K ‐function with confidence envelopes obtained from either resampling events in a nonparametric bootstrap approach, or simulating new events as in a parametric bootstrap. Methods developed are demonstrated using the locations of adult and juvenile trees in a tropical forest. A simulation study briefly examines the accuracy and power of the inferential procedures. We propose a method to test for significant differences in the levels of clustering between two spatial point processes (cases and controls) while taking into account differences in their first-order intensities. The key advance on earlier methods is that the controls are not assumed to be a Poisson process. Inference and diagnostics are based around the inhomogeneous K -function with confidence envelopes obtained from either resampling events in a nonparametric bootstrap approach, or simulating new events as in a parametric bootstrap. Methods developed are demonstrated using the locations of adult and juvenile trees in a tropical forest. A simulation study briefly examines the accuracy and power of the inferential procedures. [PUBLICATION ABSTRACT] We propose a method to test for significant differences in the levels of clustering between two spatial point processes (cases and controls) while taking into account differences in their first-order intensities. The key advance on earlier methods is that the controls are not assumed to be a Poisson process. Inference and diagnostics are based around the inhomogeneous K-function with confidence envelopes obtained from either resampling events in a nonparametric bootstrap approach, or simulating new events as in a parametric bootstrap. Methods developed are demonstrated using the locations of adult and juvenile trees in a tropical forest. A simulation study briefly examines the accuracy and power of the inferential procedures.SUMMARYWe propose a method to test for significant differences in the levels of clustering between two spatial point processes (cases and controls) while taking into account differences in their first-order intensities. The key advance on earlier methods is that the controls are not assumed to be a Poisson process. Inference and diagnostics are based around the inhomogeneous K-function with confidence envelopes obtained from either resampling events in a nonparametric bootstrap approach, or simulating new events as in a parametric bootstrap. Methods developed are demonstrated using the locations of adult and juvenile trees in a tropical forest. A simulation study briefly examines the accuracy and power of the inferential procedures. |
| Author | Henrys, P. A. Brown, P. E. |
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| Cites_doi | 10.1111/1467-842X.00002 10.1111/j.2517-6161.1955.tb00188.x 10.1111/1467-9574.00144 10.1016/j.jspi.2003.09.027 10.1111/j.2517-6161.1958.tb00272.x 10.2307/3212829 10.1111/j.1541-0420.2006.00667.x 10.1111/j.1541-0420.2006.00683.x 10.1239/aap/1059486821 10.1093/biomet/51.3-4.299 10.1198/016214507000000879 |
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| References | Guan, Y. and Loh, J. M. (2007). A thinned block bootstrap variance estimation procedure for inhomogeneous spatial point patterns. Journal of the American Statistical Association 102, 1377-1386. Diggle, P. J., Gomez-Rubio, V., Brown, P. E., Chetwynd, A. G., and Gooding, S. (2007). Second-order analysis of inhomogeneous spatial point processes using case-control data. Biometrics 63, 550-557. Waagepetersen, R. (2007). An estimating function approach to inference for inhomogeneous Neyman-Scott processes. Biometrics 63, 252-258. Cox, D. R. (1955). Some statistical methods related with series of events (with discussion). Journal of the Royal Statistical Society, Series B 17, 129-164. Møller, J. (2003). Shot noise Cox processes. Advances in Applied Probability 35, 4-26. Neyman, J. and Scott, E. L. (1958). Statistical approach to problems of cosmology. Journal of the Royal Statistical Society, Series B 20, 1-43. Schoenberg, F. P. (2004). Consistent parametric estimation of the intensity of a temporal point process. Journal of Statistical Planning and Inference 128, 79-93. Chetwynd, A. G. and Diggle, P. J. (1998). On estimating the reduced second moment measure of a stationary spatial point process. Australian and New Zealand Journal of Statistics 40, 11-15. Baddeley, A., Møller, J., and Waagepetersen, R. (2000). Non- and semi-parametric estimation of interaction in inhomogeneous point patterns. Statistica Neerlandica 54, 329-350. Diggle, P. J. (2003). Statistical Analysis of Spatial Point Patterns, 2nd edition. London : Edward Arnold. Bartlett, M. S. (1964). Spectral analysis of two dimensional point processes. Biometrics 51, 299-311. Ripley, B. D. (1976). The second order analysis of stationary point processes. Journal of Applied Probability 13, 255-266. 1955; 17 2003; 35 1958; 20 2006 2007; 102 1976; 13 2003 2007; 63 1998; 40 2004; 128 2000; 54 1964; 51 e_1_2_9_10_1 e_1_2_9_13_1 e_1_2_9_8_1 Møller J. (e_1_2_9_11_1) 2003; 35 Neyman J. (e_1_2_9_12_1) 1958; 20 e_1_2_9_5_1 e_1_2_9_4_1 e_1_2_9_3_1 e_1_2_9_2_1 Diggle P. J. (e_1_2_9_7_1) 2003 e_1_2_9_9_1 e_1_2_9_15_1 e_1_2_9_14_1 Cox D. R. (e_1_2_9_6_1) 1955; 17 |
| References_xml | – reference: Baddeley, A., Møller, J., and Waagepetersen, R. (2000). Non- and semi-parametric estimation of interaction in inhomogeneous point patterns. Statistica Neerlandica 54, 329-350. – reference: Schoenberg, F. P. (2004). Consistent parametric estimation of the intensity of a temporal point process. Journal of Statistical Planning and Inference 128, 79-93. – reference: Diggle, P. J., Gomez-Rubio, V., Brown, P. E., Chetwynd, A. G., and Gooding, S. (2007). Second-order analysis of inhomogeneous spatial point processes using case-control data. Biometrics 63, 550-557. – reference: Waagepetersen, R. (2007). An estimating function approach to inference for inhomogeneous Neyman-Scott processes. Biometrics 63, 252-258. – reference: Chetwynd, A. G. and Diggle, P. J. (1998). On estimating the reduced second moment measure of a stationary spatial point process. Australian and New Zealand Journal of Statistics 40, 11-15. – reference: Diggle, P. J. (2003). Statistical Analysis of Spatial Point Patterns, 2nd edition. London : Edward Arnold. – reference: Guan, Y. and Loh, J. M. (2007). A thinned block bootstrap variance estimation procedure for inhomogeneous spatial point patterns. Journal of the American Statistical Association 102, 1377-1386. – reference: Bartlett, M. S. (1964). Spectral analysis of two dimensional point processes. Biometrics 51, 299-311. – reference: Cox, D. R. (1955). Some statistical methods related with series of events (with discussion). Journal of the Royal Statistical Society, Series B 17, 129-164. – reference: Ripley, B. D. (1976). The second order analysis of stationary point processes. Journal of Applied Probability 13, 255-266. – reference: Møller, J. (2003). Shot noise Cox processes. Advances in Applied Probability 35, 4-26. – reference: Neyman, J. and Scott, E. L. (1958). Statistical approach to problems of cosmology. Journal of the Royal Statistical Society, Series B 20, 1-43. – volume: 63 start-page: 252 year: 2007 end-page: 258 article-title: An estimating function approach to inference for inhomogeneous Neyman‐Scott processes publication-title: Biometrics – volume: 13 start-page: 255 year: 1976 end-page: 266 article-title: The second order analysis of stationary point processes publication-title: Journal of Applied Probability – volume: 20 start-page: 1 year: 1958 end-page: 43 article-title: Statistical approach to problems of cosmology publication-title: Journal of the Royal Statistical Society, Series B – volume: 102 start-page: 1377 year: 2007 end-page: 1386 article-title: A thinned block bootstrap variance estimation procedure for inhomogeneous spatial point patterns publication-title: Journal of the American Statistical Association – volume: 63 start-page: 550 year: 2007 end-page: 557 article-title: Second‐order analysis of inhomogeneous spatial point processes using case‐control data publication-title: Biometrics – year: 2006 – year: 2003 – volume: 128 start-page: 79 year: 2004 end-page: 93 article-title: Consistent parametric estimation of the intensity of a temporal point process publication-title: Journal of Statistical Planning and Inference – volume: 17 start-page: 129 year: 1955 end-page: 164 article-title: Some statistical methods related with series of events (with discussion) publication-title: Journal of the Royal Statistical Society, Series B – volume: 40 start-page: 11 year: 1998 end-page: 15 article-title: On estimating the reduced second moment measure of a stationary spatial point process publication-title: Australian and New Zealand Journal of Statistics – volume: 54 start-page: 329 year: 2000 end-page: 350 article-title: Non‐ and semi‐parametric estimation of interaction in inhomogeneous point patterns publication-title: Statistica Neerlandica – volume: 51 start-page: 299 year: 1964 end-page: 311 article-title: Spectral analysis of two dimensional point processes publication-title: Biometrics – volume: 35 start-page: 4 year: 2003 end-page: 26 article-title: Shot noise Cox processes publication-title: Advances in Applied Probability – volume-title: Statistical Analysis of Spatial Point Patterns year: 2003 ident: e_1_2_9_7_1 – ident: e_1_2_9_5_1 doi: 10.1111/1467-842X.00002 – volume: 17 start-page: 129 year: 1955 ident: e_1_2_9_6_1 article-title: Some statistical methods related with series of events (with discussion) publication-title: Journal of the Royal Statistical Society, Series B doi: 10.1111/j.2517-6161.1955.tb00188.x – ident: e_1_2_9_3_1 – ident: e_1_2_9_2_1 doi: 10.1111/1467-9574.00144 – ident: e_1_2_9_14_1 doi: 10.1016/j.jspi.2003.09.027 – volume: 20 start-page: 1 year: 1958 ident: e_1_2_9_12_1 article-title: Statistical approach to problems of cosmology publication-title: Journal of the Royal Statistical Society, Series B doi: 10.1111/j.2517-6161.1958.tb00272.x – ident: e_1_2_9_13_1 doi: 10.2307/3212829 – ident: e_1_2_9_15_1 doi: 10.1111/j.1541-0420.2006.00667.x – ident: e_1_2_9_8_1 doi: 10.1111/j.1541-0420.2006.00683.x – ident: e_1_2_9_9_1 – volume: 35 start-page: 4 year: 2003 ident: e_1_2_9_11_1 article-title: Shot noise Cox processes publication-title: Advances in Applied Probability doi: 10.1239/aap/1059486821 – ident: e_1_2_9_4_1 doi: 10.1093/biomet/51.3-4.299 – ident: e_1_2_9_10_1 doi: 10.1198/016214507000000879 |
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| SubjectTerms | adults Algorithms Altitude Biometric Methodology Biometrics biometry Biometry - methods Biostatistics Cluster Analysis Clustering Computer Simulation Data Interpretation, Statistical diagnostic techniques Ecology Environmental epidemiology Epidemiologic Research Design Inference Inhomogeneous methods Null hypothesis P values Pattern Recognition, Automated Point estimators Poisson process Proportional Hazards Models Reproducibility of Results Risk Assessment Risk Assessment - methods Sampling distributions Sensitivity and Specificity Spatial point processes Spatial points Statistical methods Trees tropical forests |
| Title | Inference for Clustered Inhomogeneous Spatial Point Processes |
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