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An up-to-date review of scan statistics. (English) Zbl 1476.62005

Summary: Scan statistics have been a very important and active area of statistical research in the past three decades. Detecting areas with a significant concentration of points is an important task in understanding the underlying phenomena in many fields such as: epidemiology, politics, crime analysis, zoology, etc. This study reviews how scan statistics have developed in the last three decades, the main concerns of researchers in scan statistics, and how researchers have approached these concerns.

MSC:

62H11 Directional data; spatial statistics
62M30 Inference from spatial processes
62-02 Research exposition (monographs, survey articles) pertaining to statistics
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[1] Aboukhamseen, S., Soltani, A. and Najafi, M. (2016). Modelling cluster detection in spatial scan statistics: Formation of a spatial Poisson scanning window and an ADHD case study. Statistics & Probability Letters 111 26-31. · Zbl 1338.62126
[2] Adelberger, K. L., Steidel, C. C., Pettini, M., Shapley, A. E., Reddy, N. A. and Erb, D. K. (2005). The Spatial Clustering of Star-forming Galaxies at Redshifts 1.4 ≲ z ≲ 3.5. The Astrophysical Journal 619 697.
[3] Ahmed, M.-S. and Genin, M. (2020). A functional-model-adjusted spatial scan statistic. Statistics in Medicine 39 1025-1040.
[4] Allard, D. and Fraley, C. (1997). Nonparametric maximum likelihood estimation of features in spatial point processes using Voronoi tessellation. Journal of the American Statistical Association 92 1485-1493. · Zbl 0913.62090
[5] Allévius, B. and Höhle, M. (2019). An unconditional space-time scan statistic for ZIP-distributed data. Scandinavian Journal of Statistics 46 142-159. · Zbl 1420.62447
[6] Allévius, B. (2018). scanstatistics: space-time anomaly detection using scan statistics. Journal of Open Source Software 3 515.
[7] Anselin, L. (1995). Local indicators of spatial association-LISA. Geographical Analysis 27 93-115.
[8] Assunção, R. M., Souza, R. C. S. N. P. and Prates, M. O. (2020). New Frontiers for Scan Statistics: Network, Trajectory, and Text Data. In Handbook of Scan Statistics (J. Glaz and M. Koutras, eds.) 1-24. Springer New York.
[9] Assunção, R. and Correa, T. (2009). Surveillance to detect emerging space-time clusters. Computational Statistics & Data Analysis 53 2817-2830. · Zbl 1453.62033
[10] Assunção, R., Costa, M., Tavares, A. and Ferreira, S. (2006). Fast detection of arbitrarily shaped disease clusters. Statistics in Medicine 25 723-742.
[11] Assunção, R., Tavares, A., Correa, T. and Kulldorff, M. (2007). Space-time cluster identification in point processes. Canadian Journal of Statistics 35 9-25. · Zbl 1124.62065
[12] Bai, J. and Perron, P. (1998). Estimating and testing linear models with multiple structural changes. Econometrica 66 47-78. · Zbl 1056.62523
[13] Bai, J. and Perron, P. (2003). Computation and analysis of multiple structural change models. Journal of Applied Econometrics 18 1-22.
[14] Bar-Hen, A., Emily, M. and Picard, N. (2015). Spatial cluster detection using nearest neighbor distance. Spatial Statistics 14 400-411.
[15] Besag, J. and Newell, J. (1991). The detection of clusters in rare diseases. Journal of the Royal Statistical Society. Series A (Statistics in Society) 154 143-155.
[16] Bhatt, V. and Tiwari, N. (2014). A spatial scan statistic for survival data based on Weibull distribution. Statistics in Medicine 33 1867-1876.
[17] Cançado, A. L., da Silva, C. Q. and da Silva, M. F. (2014). A spatial scan statistic for zero-inflated Poisson process. Environmental and Ecological Statistics 21 627-650.
[18] Cançado, A. L., Fernandes, L. B. and da Silva, C. Q. (2017). A Bayesian spatial scan statistic for zero-inflated count data. Spatial Statistics 20 57-75.
[19] Carneiro, D. D., Bavia, M. E., Rocha, W. J., Tavares, A. C., Cardim, L. L. and Alemayehu, B. (2007). Application of spatio-temporal scan statistics for the detection of areas with increased risk for American visceral leishmaniasis in the state of Bahia, Brazil. Geospatial Health 2 113-126.
[20] Castellares, F., Prates, M. O. and Abolhassani, A. (2019). Comments on “A spatial scan statistic for compound Poisson data”. Statistics in Medicine 38 1297-1299.
[21] Chang, H.-M. and Rosychuk, R. J. (2015). A spatial scan statistic for compound Poisson data, using the negative binomial distribution and accounting for population stratification. Statistica Sinica 25 313-327. · Zbl 1480.62120
[22] Chavent, M., Kuentz, V., Labenne, A. and Saracco, J. (2017). ClustGeo: Hierarchical Clustering with Spatial Constraints R package version 2.0. · Zbl 1417.62006
[23] Choynowski, M. (1959). Maps based on probabilities. Journal of the American Statistical Association 54 385-388.
[24] Correa, T. R., Assunção, R. M. and Costa, M. A. (2015). A critical look at prospective surveillance using a scan statistic. Statistics in Medicine 34 1081-1093.
[25] Costa, M. A., Assunção, R. M. and Kulldorff, M. (2012). Constrained spanning tree algorithms for irregularly-shaped spatial clustering. Computational Statistics & Data Analysis 56 1771-1783.
[26] Cucala, L. (2008). A hypothesis-free multiple scan statistic with variable window. Biometrical Journal: Journal of Mathematical Methods in Biosciences 50 299-310. · Zbl 1442.62323
[27] Cucala, L. (2009). A flexible spatial scan test for case event data. Computational Statistics & Data Analysis 53 2843-2850. · Zbl 1208.62152
[28] Cucala, L. (2014). A distribution-free spatial scan statistic for marked point processes. Spatial Statistics 10 117-125.
[29] Cucala, L., Genin, M., Lanier, C. and Occelli, F. (2017). A multivariate Gaussian scan statistic for spatial data. Spatial Statistics 21 66-74.
[30] Culvenor, D. S., Coops, N., Preston, R. and Tolhurst, K. G. (1998). A spatial clustering approach to automated tree crown delineation. In Proc. of the International Forum on Automated Interpretation of High Spatial Resolution Digital Imagery for Forestry 67-80.
[31] de Lima, M. S., Duczmal, L. H., Neto, J. C. and Pinto, L. P. (2015). Spatial scan statistics for models with overdispersion and inflated zeros. Statistica Sinica 25 225-241. · Zbl 1480.62124
[32] de Lima, M. S., dos Santos, V. S., Duczmal, L. H. and da Silva Souza, D. (2016). A spatial scan statistic for beta regression. Spatial Statistics 18 444-454.
[33] Demattei, C. and Cucala, L. (2010). Multiple spatio-temporal cluster detection for case event data: an ordering-based approach. Communications in Statistics-Theory and Methods 40 358-372. · Zbl 1208.62102
[34] Dematteı, C., Molinari, N. and Daurès, J.-P. (2007). Arbitrarily shaped multiple spatial cluster detection for case event data. Computational Statistics & Data Analysis 51 3931-3945. · Zbl 1161.62372
[35] Desjardins, M. R., Hohl, A. and Delmelle, E. M. (2020). Rapid surveillance of COVID-19 in the United States using a prospective space-time scan statistic: Detecting and evaluating emerging clusters. Applied Geography 118 102202.
[36] Duczmal, L., Cançado, A. L., Takahashi, R. H. and Bessegato, L. F. (2007). A genetic algorithm for irregularly shaped spatial scan statistics. Computational Statistics & Data Analysis 52 43-52. · Zbl 1452.62804
[37] Duczmal, L. H., Moreira, G. J., Burgarelli, D., Takahashi, R. H., Magalhães, F. C. and Bodevan, E. C. (2011). Voronoi distance based prospective space-time scans for point data sets: a dengue fever cluster analysis in a southeast Brazilian town. International Journal of Health Geographics 10 29.
[38] Dwass, M. (1957). Modified randomization tests for nonparametric hypotheses. The Annals of Mathematical Statistics 28 181-187. · Zbl 0088.35301
[39] Eck, J., Chainey, S., Cameron, J. and Wilson, R. (2005). Mapping Crime: Understanding Hotspots.
[40] Elias, J., Harmsen, D., Claus, H., Hellenbrand, W., Frosch, M. and Vogel, U. (2006). Spatiotemporal analysis of invasive meningococcal disease, Germany. Emerging Infectious Diseases 12 1689.
[41] Erdos, P. and Rényi, A. (1960). On the evolution of random graphs. Publications of the Mathematical Institute of the Hungarian Academy of Sciences 5 17-60. · Zbl 0103.16301
[42] Fortunato, S. (2010). Community detection in graphs. Physics Reports 486 75-174.
[43] French, J. (2020a). smerc: Statistical Methods for Regional Counts R package version 1.3.3.
[44] French, J. (2020b). smacpod: Statistical Methods for the Analysis of Case-Control Point Data R package version 2.1.
[45] Gangnon, R. E. (2010a). Local multiplicity adjustments for spatial cluster detection. Environmental and Ecological Statistics 17 55-71.
[46] Gangnon, R. E. (2010b). A model for space-time cluster detection using spatial clusters with flexible temporal risk patterns. Statistics in Medicine 29 2325-2337.
[47] Gangnon, R. E. and Clayton, M. K. (2000). Bayesian detection and modeling of spatial disease clustering. Biometrics 56 922-935. · Zbl 1060.62610
[48] Gangnon, R. E. and Clayton, M. K. (2001). A weighted average likelihood ratio test for spatial clustering of disease. Statistics in Medicine 20 2977-2987.
[49] Gangnon, R. E. and Clayton, M. K. (2003). A hierarchical model for spatially clustered disease rates. Statistics in Medicine 22 3213-3228.
[50] Gangnon, R. E. and Clayton, M. K. (2004). Likelihood-based tests for localized spatial clustering of disease. Environmetrics: The Official Journal of the International Environmetrics Society 15 797-810.
[51] Gangnon, R. and Clayton, M. K. (2007). Cluster detection using Bayes factors from overparameterized cluster models. Environmental and Ecological Statistics 14 69-82.
[52] Garwood, F. (1936). Fiducial limits for the Poisson distribution. Biometrika 28 437-442. · JFM 62.0598.03
[53] Gladders, M. D. and Yee, H. (2000). A new method for galaxy cluster detection. I. The algorithm. The Astronomical Journal 120 2148.
[54] Gómez-Rubio, V. and López-Quílez, A. (2010). Statistical methods for the geographical analysis of rare diseases. Advances in Experimental Medicine and Biology 686 151-171.
[55] Gómez-Rubio, V., Moraga, P., Molitor, J. and Rowlingson, B. (2019). DClusterm: model-based detection of disease clusters R package version 0.2-3.
[56] Goura, V., Rao, N. M. and Reddy, M. R. (2011). A dynamic clustering technique using minimumspanning tree. In Proceedings of the 2nd International Conference on Biotechnology and Food Science (IPCBEE’11), IACSIT Press, Singapore 66-70.
[57] Green, P. J. (1995). Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika 82 711-732. · Zbl 0861.62023
[58] Grubesic, T. H. (2006). On the application of fuzzy clustering for crime hot spot detection. Journal of Quantitative Criminology 22 77.
[59] Gutteridge, A., Bartlett, G. J. and Thornton, J. M. (2003). Using a neural network and spatial clustering to predict the location of active sites in enzymes. Journal of Molecular Biology 330 719-734.
[60] Gómez-Rubio, V., Ferrándiz-Ferragud, J. and Lopez-Quílez, A. (2005). Detecting clusters of disease with R. Journal of Geographical Systems 7 189-206.
[61] Han, J., Kamber, M. and Tung, A. K. H. Spatial Clustering Methods in Data Mining. In Geographic Data Mining and Knowledge Discovery 188-217. Taylor & Francis.
[62] Haralick, R. and Dinstein, I. (1975). A spatial clustering procedure for multi-image data. IEEE Transactions on Circuits and Systems 22 440-450.
[63] Haralick, R. and Kelly, G. (1969). Pattern recognition with measurement space and spatial clustering for multiple images. Proceedings of the IEEE 57 654-665.
[64] Harries, K. D. (1999). Mapping Crime: Principle and Practice Technical Report, US Department of Justice, Office of Justice Programs, National Institute of Justice, Crime Mapping Research Center.
[65] Huang, L., Kulldorff, M. and Gregorio, D. (2007). A spatial scan statistic for survival data. Biometrics 63 109-118. · Zbl 1124.62076
[66] Huang, L., Tiwari, R. C., Zou, Z., Kulldorff, M. and Feuer, E. J. (2009). Weighted normal spatial scan statistic for heterogeneous population data. Journal of the American Statistical Association 104 886-898. · Zbl 1388.62186
[67] Ishioka, F., Kawahara, J., Mizuta, M., Minato, S.-i. and Kurihara, K. (2019). Evaluation of hotspot cluster detection using spatial scan statistic based on exact counting. Japanese Journal of Statistics and Data Science 2 241-262. · Zbl 1430.62230
[68] Izakian, H. and Pedrycz, W. (2012). A new PSO-optimized geometry of spatial and spatio-temporal scan statistics for disease outbreak detection. Swarm and Evolutionary Computation 4 1-11.
[69] Jaccard, P. (1901). Distribution de la flore alpine dans le bassin des Dranses et dans quelques régions voisines. Bull Soc Vaudoise Sci Nat 37 241-272.
[70] Jain, A. K. and Dubes, R. C. (1988). Algorithms for clustering data. Prentice-Hall, Inc., New Jersey. · Zbl 0665.62061
[71] Jung, I. (2019). Spatial scan statistics for matched case-control data. PloS One 14 e0221225.
[72] Jung, I. and Cho, H. J. (2015). A nonparametric spatial scan statistic for continuous data. International Journal of Health Geographics 14 30.
[73] Jung, I., Kulldorff, M. and Klassen, A. C. (2007). A spatial scan statistic for ordinal data. Statistics in Medicine 26 1594-1607.
[74] Jung, I., Kulldorff, M. and Richard, O. J. (2010). A spatial scan statistic for multinomial data. Statistics in Medicine 29 1910-1918.
[75] Kenett, R. S. and Pollak, M. (1996). Data-analytic aspects of the Shiryayev-Roberts control chart: Surveillance of a non-homogeneous Poisson process. Journal of Applied Statistics 23 125-138.
[76] Kim, A. Y. and Wakefield, J. (2018). SpatialEpi: Methods and Data for Spatial Epidemiology R package version 1.2.3.
[77] Kim, R. S. J., Kepner, J. V., Postman, M., Strauss, M. A., Bahcall, N. A., Gunn, J. E., Lupton, R. H., Annis, J., Nichol, R. C., Castander, F. J. et al. (2002). Detecting clusters of galaxies in the sloan digital sky survey. i. monte carlo comparison of cluster detection algorithms. The Astronomical Journal 123 20.
[78] Kleinman, K. (2015). rsatscan: Tools, Classes, and Methods for Interfacing with SaTScan Stand-Alone Software R package version 0.3.9200.
[79] Knox, E. and Bartlett, M. (1964). The detection of space-time interactions. Journal of the Royal Statistical Society. Series C (Applied Statistics) 13 25-30.
[80] Kulldorff, M. (1997). A spatial scan statistic. Communications in Statistics-Theory and Methods 26 1481-1496. · Zbl 0920.62116
[81] Kulldorff, M. (2001). Prospective time periodic geographical disease surveillance using a scan statistic. Journal of the Royal Statistical Society: Series A (Statistics in Society) 164 61-72. · Zbl 1002.62517
[82] Kulldorff, M., Fang, Z. and Walsh, S. J. (2003). A tree-based scan statistic for database disease surveillance. Biometrics 59 323-331. · Zbl 1210.62177
[83] Kulldorff, M., Huang, L. and Konty, K. (2009). A scan statistic for continuous data based on the normal probability model. International Journal of Health Geographics 8 58.
[84] Kulldorff, M. and Nagarwalla, N. (1995). Spatial disease clusters: detection and inference. Statistics in Medicine 14 799-810.
[85] Kulldorff, M., Athas, W. F., Feurer, E. J., Miller, r. A. and Key, C. R. (1998). Evaluating cluster alarms: a space-time scan statistic and brain cancer in Los Alamos, New Mexico. American Journal of Public Health 88 1377-1380.
[86] Kulldorff, M., Huang, L., Pickle, L. and Duczmal, L. (2006). An elliptic spatial scan statistic. Statistics in Medicine 25 3929-3943.
[87] Lambert, D. (1992). Zero-inflated Poisson regression, with an application to defects in manufacturing. Technometrics 34 1-14. · Zbl 0850.62756
[88] Lee, J., Gangnon, R. E. and Zhu, J. (2017). Cluster detection of spatial regression coefficients. Statistics in Medicine 36 1118-1133.
[89] Lee, M. and Jung, I. (2019). Modified spatial scan statistics using a restricted likelihood ratio for ordinal outcome data. Computational Statistics & Data Analysis 133 28-39. · Zbl 07027243
[90] Lee, J., Sun, Y. and Chang, H. H. (2020). Spatial cluster detection of regression coefficients in a mixed-effects model. Environmetrics 31 e2578.
[91] Lee, J., Gangnon, R. E., Zhu, J. and Liang, J. (2017). Uncertainty of a detected spatial cluster in 1D: Quantification and visualization. Stat 6 345-359.
[92] Lee, J., Kamenetsky, M. E., Gangnon, R. E. and Zhu, J. (2021). Clustered spatio-temporal varying coefficient regression model. Statistics in Medicine 40 465-480.
[93] Li, X.-Z., Wang, J.-F., Yang, W.-Z., Li, Z.-J. and Lai, S.-J. (2011). A spatial scan statistic for multiple clusters. Mathematical Biosciences 233 135-142. · Zbl 1226.92039
[94] Li, M., Shi, X., Li, X., Ma, W., He, J. and Liu, T. (2019). Sensitivity of disease cluster detection to spatial scales: an analysis with the spatial scan statistic method. International Journal of Geographical Information Science 33 2125-2152.
[95] Liu, Y., Liu, Y. and Zhang, T. (2018). Wald-based spatial scan statistics for cluster detection. Computational Statistics & Data Analysis 127 298-310. · Zbl 1469.62108
[96] Liverani, S., Hastie, D. I., Azizi, L., Papathomas, M. and Richardson, S. (2015). PReMiuM: An R Package for Profile Regression Mixture Models Using Dirichlet Processes. Journal of Statistical Software 64 1-30.
[97] Loche, R., Giron, B., Abrial, D., Cucala, L., Charras-Garrido, M. and De-Goer, J. (2016). graphscan: Cluster Detection with Hypothesis Free Scan Statistic R package version 1.1.1.
[98] Mantel, N. (1967). The detection of disease clustering and a generalized regression approach. Cancer Research 27 209-220.
[99] Marchette, D. (2012). Scan statistics on graphs. Wiley Interdisciplinary Reviews: Computational Statistics 4 466-473.
[100] Meyer, S., Held, L., Höhle, M. et al. (2017). Spatio-Temporal Analysis of Epidemic Phenomena Using the R Package surveillance. Journal of Statistical Software 77 1-55.
[101] Minato, S.-i. (1993). Zero-suppressed BDDs for set manipulation in combinatorial problems. In Proceedings of the 30th International Design Automation Conference 272-277.
[102] Mo, H. and White, S. D. (1996). An analytic model for the spatial clustering of dark matter haloes. Monthly Notices of the Royal Astronomical Society 282 347-361.
[103] Molinari, N., Bonaldi, C. and Daurés, J.-P. (2001). Multiple temporal cluster detection. Biometrics 57 577-583. · Zbl 1209.62315
[104] Moraga, P. (2017). SpatialEpiApp: A Shiny Web Application for the Analysis of Spatial and Spatio-Temporal Disease Data R package version 0.3.
[105] Murray, A. T. and Estivill-Castro, V. (1998). Cluster discovery techniques for exploratory spatial data analysis. International Journal of Geographical Information Science 12 431-443.
[106] Murray, A. T., Grubesic, T. H. and Wei, R. (2014). Spatially significant cluster detection. Spatial Statistics 10 103-116.
[107] Myers, N., Mittermeier, R. A., Mittermeier, C. G., Da Fonseca, G. A. and Kent, J. (2000). Biodiversity hotspots for conservation priorities. Nature 403 853.
[108] Neill, D. B. (2011). Fast Bayesian scan statistics for multivariate event detection and visualization. Statistics in Medicine 30 455-469.
[109] Neill, D. B. (2012). Fast subset scan for spatial pattern detection. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 74 337-360. · Zbl 1411.94028
[110] Neill, D. B. and Cooper, G. F. (2010). A multivariate Bayesian scan statistic for early event detection and characterization. Machine Learning 79 261-282. · Zbl 1475.62238
[111] Neill, D., Moore, A. and Cooper, G. (2005). A Bayesian spatial scan statistic. Advances in Neural Information Processing Systems 18 1003-1010.
[112] Openshaw, S., Charlton, M., Wymer, C. and Craft, A. (1987). A mark 1 geographical analysis machine for the automated analysis of point data sets. International Journal of Geographical Information System 1 335-358.
[113] Ord, J. K. and Getis, A. (1995). Local spatial autocorrelation statistics: distributional issues and an application. Geographical Analysis 27 286-306.
[114] Otani, T. and Takahashi, K. (2020). rflexscan: The Flexible Spatial Scan Statistic R package version 0.3.1.
[115] Prates, M. O., Assunção, R. M. and Costa, M. A. (2012). Flexible scan statistic test to detect disease clusters in hierarchical trees. Computational Statistics 27 715-737. · Zbl 1304.65062
[116] Prates, M. O., Kulldorff, M. and Assuncao, R. M. (2014). Relative risk estimates from spatial and space-time scan statistics: are they biased? Statistics in Medicine 33 2634-2644.
[117] Priebe, C. E., Conroy, J. M., Marchette, D. J. and Park, Y. (2005). Scan statistics on enron graphs. Computational & Mathematical Organization Theory 11 229-247. · Zbl 1086.68562
[118] Prim, R. C. (1957). Shortest connection networks and some generalizations. Bell System Technical Journal 36 1389-1401.
[119] Ross, S. M. (2014). Introduction to Probability Models. Academic Press.
[120] Rosychuk, R. J., Huston, C. and Prasad, N. G. (2006). Spatial event cluster detection using a compound Poisson distribution. Biometrics 62 465-470. · Zbl 1097.62135
[121] Sherman, L. W. and Weisburd, D. (1995). General deterrent effects of police patrol in crime “hot spots”: A randomized, controlled trial. Justice quarterly 12 625-648.
[122] Sierksma, G. and Hoogeveen, H. (1991). Seven criteria for integer sequences being graphic. Journal of Graph Theory 15 223-231. · Zbl 0752.05052
[123] Soltani, A. and Aboukhamseen, S. (2015). An alternative cluster detection test in spatial scan statistics. Communications in Statistics-Theory and Methods 44 1592-1601. · Zbl 1320.62120
[124] Stohlgren, T. J., Binkley, D., Chong, G. W., Kalkhan, M. A., Schell, L. D., Bull, K. A., Otsuki, Y., Newman, G., Bashkin, M. and Son, Y. (1999). Exotic plant species invade hot spots of native plant diversity. Ecological Monographs 69 25-46.
[125] Streit, R. (2010). Poisson Point Processes Imaging, Tracking, and Sensing. Springer, New York.
[126] Tango, T. (2008). A spatial scan statistic with a restricted likelihood ratio. Japanese Journal of Biometrics 29 75-95.
[127] Tango, T. (2016). On the recent debate on the space-time scan statistic for prospective surveillance. Statistics in Medicine 35 1927.
[128] Tango, T. and Takahashi, K. (2005). A flexibly shaped spatial scan statistic for detecting clusters. International Journal of Health Geographics 4 11.
[129] Tango, T., Takahashi, K. and Kohriyama, K. (2011). A space-time scan statistic for detecting emerging outbreaks. Biometrics 67 106-115. · Zbl 1218.62120
[130] Tonini, M., Tuia, D. and Ratle, F. (2009). Detection of clusters using space-time scan statistics. International Journal of Wildland Fire 18 830-836.
[131] Turnbull, B. W., Iwano, E. J., Burnett, W. S., Howe, H. L. and Clark, L. C. (1989). Monitoring for clusters of disease; Application to leukemia incidence in upstate New York Technical Report, Cornell University Operations Research and Industrial Engineering.
[132] Valles, G. (2014). AMOEBA: A Multidirectional Optimum Ecotope-Based Algorithm R package version 1.1.
[133] Veloso, B. M., Correa, T. R., Prates, M. O., Oliveira, G. F. and Tavares, A. I. (2017). MAD-STEC: a method for multiple automatic detection of space-time emerging clusters. Statistics and Computing 27 1099-1110. · Zbl 1384.62205
[134] Wakefield, J. and Kim, A. (2013). A Bayesian model for cluster detection. Biostatistics 14 752-765.
[135] Waller, L. A., Carlin, B. P., Xia, H. and Gelfand, A. E. (1997). Hierarchical spatio-temporal mapping of disease rates. Journal of the American Statistical Association 92 607-617. · Zbl 0889.62094
[136] Wan, Y., Pei, T., Zhou, C., Jiang, Y., Qu, C. and Qiao, Y. (2012). ACOMCD: A multiple cluster detection algorithm based on the spatial scan statistic and ant colony optimization. Computational Statistics & Data Analysis 56 283-296.
[137] Wang, T.-C., Hsu, T.-C. and Phoa, F. K. H. (2016). SNscan: Scan Statistics in Social Networks R package version 1.0.
[138] Wang, T.-C. and Phoa, F. K. H. (2016). A scanning method for detecting clustering pattern of both attribute and structure in social networks. Physica A: Statistical Mechanics and its Applications 445 295-309.
[139] Wang, B., Phillips, J. M., Schreiber, R., Wilkinson, D., Mishra, N. and Tarjan, R. (2008). Spatial scan statistics for graph clustering. In Proceedings of the 2008 SIAM International Conference on Data Mining 727-738. SIAM.
[140] Wieland, S. C., Brownstein, J. S., Berger, B. and Mandl, K. D. (2007). Density-equalizing Euclidean minimum spanning trees for the detection of all disease cluster shapes. Proceedings of the National Academy of Sciences 104 9404-9409. · Zbl 1156.62369
[141] Woodall, W. H., Zhao, M. J., Paynabar, K., Sparks, R. and Wilson, J. D. (2017). An overview and perspective on social network monitoring. IISE Transactions 49 354-365.
[142] Wu, T.-L. and Glaz, J. (2015). A new adaptive procedure for multiple window scan statistics. Computational Statistics & Data Analysis 82 164-172. · Zbl 06984113
[143] Xu, J. and Gangnon, R. E. (2016). Stepwise and stagewise approaches for spatial cluster detection. Spatial and Spatio-temporal Epidemiology 17 59-74.
[144] Yamada, I. and Rogerson, P. (2008). Statistical detection and surveillance of geographic clusters. Chapman and Hall/CRC. · Zbl 1159.86001
[145] Yan, P. and Clayton, M. K. (2006). A cluster model for space-time disease counts. Statistics in Medicine 25 867-881.
[146] Yin, P. and Mu, L. (2018). A hybrid method for fast detection of spatial disease clusters in irregular shapes. GeoJournal 83 693-705.
[147] Zhang, Z., Assunção, R. and Kulldorff, M. (2010). Spatial scan statistics adjusted for multiple clusters. Journal of Probability and Statistics, Article ID 642379 2010 1-11. · Zbl 1200.62091
[148] Zhang, T. and Lin, G. (2009). Spatial scan statistics in loglinear models. Computational Statistics & Data Analysis 53 2851-2858. · Zbl 1453.62264
[149] Zhang, T. and Lin, G. (2014). Family of power divergence spatial scan statistics. Computational Statistics & Data Analysis 75 162-178. · Zbl 06983952
[150] Zhang, T., Lin, G. et al. (2017). Asymptotic properties of spatial scan statistics under the alternative hypothesis. Bernoulli 23 89-109. · Zbl 1459.62126
[151] Zhang, T., Zhang, Z. and Lin, G. (2012). Spatial scan statistics with overdispersion. Statistics in Medicine 31 762-774.
[152] Zhang, L. and Zhu, Z. (2012). Spatial multiresolution cluster detection method. arXiv preprint arXiv:1205.2106. · Zbl 1327.62385
[153] Zhou, Y., Cheng, H. and Yu, J. X. (2009). Graph clustering based on structural/attribute similarities. Proceedings of the VLDB Endowment 2 718-729.
[154] Zhou, R., Shu, L. and Su, Y. (2015). An adaptive minimum spanning tree test for detecting irregularly-shaped spatial clusters. Computational Statistics & Data Analysis 89 134-146. · Zbl 1468.62241
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