Second‐order analysis of inhomogeneous spatio‐temporal point process data
Present address: IUT STID ‐ LANLG, Université d'Avignon, BP 1207, 84 911 Avignon, France.
Abstract
Second‐order methods provide a natural starting point for the analysis of spatial point process data. In this note we extend to the spatio‐temporal setting a method proposed by Baddeley et al. [Statistica Neerlandica (2000) Vol. 54, pp. 329–350] for inhomogeneous spatial point process data, and apply the resulting estimator to data on the spatio‐temporal distribution of human Campylobacter infections in an area of north‐west England.
Citing Literature
Number of times cited according to CrossRef: 58
- I. Fuentes-Santos, W. González-Manteiga, J.P. Zubelli, Nonparametric spatiotemporal analysis of violent crime. A case study in the Rio de Janeiro metropolitan area, Spatial Statistics, 10.1016/j.spasta.2020.100431, (100431), (2020).
- Timothy M. Pollington, Michael J. Tildesley, T. Déirdre Hollingsworth, Lloyd A.C. Chapman, Developments in statistical inference when assessing spatiotemporal disease clustering with the tau statistic, Spatial Statistics, 10.1016/j.spasta.2020.100438, (100438), (2020).
- Fekadu L. Bayisa, Markus Ådahl, Patrik Rydén, Ottmar Cronie, Large-scale modelling and forecasting of ambulance calls in northern Sweden using spatio-temporal log-Gaussian Cox processes, Spatial Statistics, 10.1016/j.spasta.2020.100471, (100471), (2020).
- Álvaro Briz-Redón, Francisco Martínez-Ruiz, Francisco Montes, Adjusting the Knox test by accounting for spatio-temporal crime risk heterogeneity to analyse near-repeats, European Journal of Criminology, 10.1177/1477370820905106, (147737082090510), (2020).
- Jonatan A. González, Ute Hahn, Jorge Mateu, Analysis of tornado reports through replicated spatiotemporal point patterns, Journal of the Royal Statistical Society: Series C (Applied Statistics), 10.1111/rssc.12375, 69, 1, (3-23), (2019).
- Woongsoon Jang, Bianca N.I. Eskelson, Tasha Murray, Ken B. Crosby, Shannon Wagner, Erin Gorby, Neal W. Aven, Relationships between invasive plant species occurrence and socio-economic variables in urban green spaces of southeastern British Columbia, Canada, Urban Forestry & Urban Greening, 10.1016/j.ufug.2019.126527, (126527), (2019).
- Jorge Mateu, Mehdi Moradi, Ottmar Cronie, Spatio-temporal point patterns on linear networks: Pseudo-separable intensity estimation, Spatial Statistics, 10.1016/j.spasta.2019.100400, (100400), (2019).
- Giada Adelfio, Marianna Siino, Jorge Mateu, Francisco J. Rodríguez-Cortés, Some properties of local weighted second-order statistics for spatio-temporal point processes, Stochastic Environmental Research and Risk Assessment, 10.1007/s00477-019-01748-1, (2019).
- Jesper Møller, Heidi S. Christensen, Francisco Cuevas-Pacheco, Andreas D. Christoffersen, Structured Space-Sphere Point Processes and K-Functions, Methodology and Computing in Applied Probability, 10.1007/s11009-019-09712-w, (2019).
- M. Mehdi Moradi, Jorge Mateu, First and second-order characteristics of spatio-temporal point processes on linear networks, Journal of Computational and Graphical Statistics, 10.1080/10618600.2019.1694524, (1-28), (2019).
- A. Iftimi, O. Cronie, F. Montes, Second‐order analysis of marked inhomogeneous spatiotemporal point processes: Applications to earthquake data, Scandinavian Journal of Statistics, 10.1111/sjos.12367, 46, 3, (661-685), (2018).
- Marianna Siino, Giada Adelfio, Jorge Mateu, Joint second-order parameter estimation for spatio-temporal log-Gaussian Cox processes, Stochastic Environmental Research and Risk Assessment, 10.1007/s00477-018-1579-0, 32, 12, (3525-3539), (2018).
- Robert Fletcher, Marie-Josée Fortin, Robert Fletcher, Marie-Josée Fortin, Spatial Dispersion and Point Data, Spatial Ecology and Conservation Modeling, 10.1007/978-3-030-01989-1, (101-132), (2018).
- Adina Iftimi, Marie-Colette van Lieshout, Francisco Montes, A multi-scale area-interaction model for spatio-temporal point patterns, Spatial Statistics, 10.1016/j.spasta.2018.06.001, 26, (38-55), (2018).
- M. N. M. Lieshout, Nonparametric indices of dependence between components for inhomogeneous multivariate random measures and marked sets, Scandinavian Journal of Statistics, 10.1111/sjos.12331, 45, 4, (985-1015), (2018).
- C. Comas, J. Conde, J. Mateu, A second-order test to detect spatio-temporal anisotropic effects in point patterns, Statistics, 10.1080/02331888.2018.1469633, 52, 4, (717-733), (2018).
- Marianna Siino, Francisco J. Rodríguez‐Cortés, Jorge Mateu, Giada Adelfio, Testing for local structure in spatiotemporal point pattern data, Environmetrics, 10.1002/env.2463, 29, 5-6, (2017).
- Isabel Fuentes‐Santos, Wenceslao González‐Manteiga, Jorge Mateu, A first‐order, ratio‐based nonparametric separability test for spatiotemporal point processes, Environmetrics, 10.1002/env.2482, 29, 1, (2017).
- Zhilin Li, Qiliang Liu, Jianbo Tang, Min Deng, An adaptive method for clustering spatio‐temporal events, Transactions in GIS, 10.1111/tgis.12312, 22, 1, (323-347), (2017).
- Edith Gabriel, Spatiotemporal Point Pattern Analysis and Modeling, Encyclopedia of GIS, 10.1007/978-3-319-17885-1, (2161-2168), (2017).
- Reem Y. Ali, Venkata M. V. Gunturi, Andrew J. Kotz, Emre Eftelioglu, Shashi Shekhar, William F. Northrop, Discovering non-compliant window co-occurrence patterns, GeoInformatica, 10.1007/s10707-016-0289-3, 21, 4, (829-866), (2017).
- Xinyue Ye, Ling Wu, Jay Lee, Accounting for Spatiotemporal Inhomogeneity of Urban Crime in China, Papers in Applied Geography, 10.1080/23754931.2016.1268969, 3, 2, (196-205), (2017).
- Jiří Dvořák, Michaela Prokešová, Asymptotic properties of the minimum contrast estimators for projections of inhomogeneous space-time shot-noise Cox processes, Applications of Mathematics, 10.1007/s10492-016-0138-6, 61, 4, (387-411), (2016).
- Sebastian Meyer, Ingeborg Warnke, Wulf Rössler, Leonhard Held, Model-based testing for space–time interaction using point processes: An application to psychiatric hospital admissions in an urban area, Spatial and Spatio-temporal Epidemiology, 10.1016/j.sste.2016.03.002, 17, (15-25), (2016).
- A. Stein, Discussion of “Spatial statistics: Marks, maps and shapes”, Quality Engineering, 10.1080/08982112.2015.1100460, 28, 1, (96-97), (2016).
- Jack D. Hywood, Mark N. Read, Gregory Rice, Statistical analysis of spatially homogeneous dynamic agent-based processes using functional time series analysis, Spatial Statistics, 10.1016/j.spasta.2016.06.002, 17, (199-219), (2016).
- Jesper Møller, Farzaneh Safavimanesh, Jakob Gulddahl Rasmussen, The cylindrical $K$-function and Poisson line cluster point processes, Biometrika, 10.1093/biomet/asw044, 103, 4, (937-954), (2016).
- Alexander Hohl, Eric Delmelle, Wenwu Tang, Irene Casas, Accelerating the discovery of space-time patterns of infectious diseases using parallel computing, Spatial and Spatio-temporal Epidemiology, 10.1016/j.sste.2016.05.002, 19, (10-20), (2016).
- Jonatan A. González, Francisco J. Rodríguez-Cortés, Ottmar Cronie, Jorge Mateu, Spatio-temporal point process statistics: A review, Spatial Statistics, 10.1016/j.spasta.2016.10.002, 18, (505-544), (2016).
- Oliver Nakoinz, Daniel Knitter, Oliver Nakoinz, Daniel Knitter, Point Pattern, Modelling Human Behaviour in Landscapes, 10.1007/978-3-319-29538-1_7, (129-147), (2016).
- Jiří Dvořák, Michaela Prokešová, Parameter Estimation for Inhomogeneous Space‐Time Shot‐Noise Cox Point Processes, Scandinavian Journal of Statistics, 10.1111/sjos.12222, 43, 4, (939-961), (2016).
- Sergi Costafreda-Aumedes, Carles Comas, Cristina Vega-Garcia, Spatio-Temporal Configurations of Human-Caused Fires in Spain through Point Patterns, Forests, 10.3390/f7090185, 7, 12, (185), (2016).
- Pablo Valdes-Donoso, Lovell S. Jarvis, Dave Wright, Julio Alvarez, Andres M. Perez, Measuring Progress on the Control of Porcine Reproductive and Respiratory Syndrome (PRRS) at a Regional Level: The Minnesota N212 Regional Control Project (Rcp) as a Working Example, PLOS ONE, 10.1371/journal.pone.0149498, 11, 2, (e0149498), (2016).
- O. Cronie, M. N. M. van Lieshout, Summary statistics for inhomogeneous marked point processes, Annals of the Institute of Statistical Mathematics, 10.1007/s10463-015-0515-z, 68, 4, (905-928), (2015).
- Edith Gabriel, Spatio-Temporal Point Pattern Analysis and Modeling, Encyclopedia of GIS, 10.1007/978-3-319-23519-6, (1-8), (2015).
- Reem Y. Ali, Venkata M.V. Gunturi, Andrew J. Kotz, Shashi Shekhar, William F. Northrop, Discovering Non-compliant Window Co-Occurrence Patterns: A Summary of Results, Advances in Spatial and Temporal Databases, 10.1007/978-3-319-22363-6_21, (391-410), (2015).
- O. Cronie, M. N. M. Van Lieshout, A ‐function for Inhomogeneous Spatio‐temporal Point Processes, Scandinavian Journal of Statistics, 10.1111/sjos.12123, 42, 2, (562-579), (2014).
- C. Comas, F. J. Rodriguez‐Cortes, J. Mateu, Second‐order analysis of anisotropic spatiotemporal point process data, Statistica Neerlandica, 10.1111/stan.12046, 69, 1, (49-66), (2014).
- Ibon Tamayo-Uria, Jorge Mateu, Peter J. Diggle, Modelling of the spatio-temporal distribution of rat sightings in an urban environment, Spatial Statistics, 10.1016/j.spasta.2014.03.005, 9, (192-206), (2014).
- John A. Long, Rick L. Lawrence, Perry R. Miller, Lucy A. Marshall, Mark C. Greenwood, Adoption of cropping sequences in northeast Montana: A spatio-temporal analysis, Agriculture, Ecosystems & Environment, 10.1016/j.agee.2014.07.022, 197, (77-87), (2014).
- Giuseppe Arbia, Giuseppe Espa, Diego Giuliani, Maria Michela Dickson, Spatio-temporal clustering in the pharmaceutical and medical device manufacturing industry: A geographical micro-level analysis, Regional Science and Urban Economics, 10.1016/j.regsciurbeco.2014.10.001, 49, (298-304), (2014).
- Jorge Mateu, Francisco J. Rodríguez-Cortés, Local Clustering in Spatio-Temporal Point Patterns, Mathematics of Planet Earth, 10.1007/978-3-642-32408-6_40, (171-174), (2014).
- Frederic Paik Schoenberg, David R. Brillinger, Peter Guttorp, Point Processes, Spatial‐Temporal, Wiley StatsRef: Statistics Reference Online, 10.1002/9781118445112, (2014).
- C. Comas, S. Costafreda-Aumedes, C. Vega-Garcia, Characterizing configurations of fire ignition points through spatiotemporal point processes, Natural Hazards and Earth System Sciences Discussions, 10.5194/nhessd-2-2891-2014, 2, 4, (2891-2911), (2014).
- J. Møller, M. Ghorbani, Functional summary statistics for the Johnson–Mehl model, Journal of Statistical Computation and Simulation, 10.1080/00949655.2013.850691, 85, 5, (899-916), (2013).
- Michaela Prokešová, Jiří Dvořák, Statistics for Inhomogeneous Space-Time Shot-Noise Cox Processes, Methodology and Computing in Applied Probability, 10.1007/s11009-013-9324-0, 16, 2, (433-449), (2013).
- Edith Gabriel, Estimating Second-Order Characteristics of Inhomogeneous Spatio-Temporal Point Processes, Methodology and Computing in Applied Probability, 10.1007/s11009-013-9358-3, 16, 2, (411-431), (2013).
- Eugenia Nissi, Annalina Sarra, Sergio Palermi, Gaetano De Luca, The Application of M-Function Analysis to the Geographical Distribution of Earthquake Sequence, Classification and Data Mining, 10.1007/978-3-642-28894-4_32, (271-278), (2013).
- Roger S. Bivand, Edzer Pebesma, Virgilio Gómez-Rubio, Roger S. Bivand, Edzer Pebesma, Virgilio Gómez-Rubio, Spatial Point Pattern Analysis, Applied Spatial Data Analysis with R, 10.1007/978-1-4614-7618-4, (173-211), (2013).
- Mohammad Ghorbani, Testing the weak stationarity of a spatio-temporal point process, Stochastic Environmental Research and Risk Assessment, 10.1007/s00477-012-0597-6, 27, 2, (517-524), (2012).
- Alexandre Rodrigues, Peter J. Diggle, Bayesian Estimation and Prediction for Inhomogeneous Spatiotemporal Log-Gaussian Cox Processes Using Low-Rank Models, With Application to Criminal Surveillance, Journal of the American Statistical Association, 10.1080/01621459.2011.644496, 107, 497, (93-101), (2012).
- M. N. M. van Lieshout, A. Stein, Earthquake Modelling at the Country Level Using Aggregated Spatio-Temporal Point Processes, Mathematical Geosciences, 10.1007/s11004-011-9380-3, 44, 3, (309-326), (2012).
- G. Arbia, G. Espa, D. Giuliani, A. Mazzitelli, Clusters of firms in an inhomogeneous space: The high-tech industries in Milan, Economic Modelling, 10.1016/j.econmod.2011.01.012, 29, 1, (3-11), (2012).
- Jesper Møller, Mohammad Ghorbani, Aspects of second‐order analysis of structured inhomogeneous spatio‐temporal point processes, Statistica Neerlandica, 10.1111/j.1467-9574.2012.00526.x, 66, 4, (472-491), (2012).
- M. N. M. van Lieshout, A J–function for inhomogeneous point processes, Statistica Neerlandica, 10.1111/j.1467-9574.2011.00482.x, 65, 2, (183-201), (2011).
- E. GABRIEL, D. J. WILSON, A. J. H. LEATHERBARROW, J. CHEESBROUGH, S. GEE, E. BOLTON, A. FOX, P. FEARNHEAD, C. A. HART, P. J. DIGGLE, Spatio-temporal epidemiology of Campylobacter jejuni enteritis, in an area of Northwest England, 2000–2002, Epidemiology and Infection, 10.1017/S0950268810000488, 138, 10, (1384-1390), (2010).
- Edith Gabriel, Peter J. Diggle, Second-Order Analysis of the Spatio-temporal Distribution of Human Campylobacteriosis in Preston, Lancashire, geoENV VII – Geostatistics for Environmental Applications, 10.1007/978-90-481-2322-3_9, (99-106), (2010).
- Frederic Paik Schoenberg, David R. Brillinger, Peter Guttorp, Point Processes, Spatial‐Temporal , Encyclopedia of Environmetrics, 10.1002/9780470057339, (2006).
