References
- Bach, F. (2013), Learning with Submodular Functions: A Convex Optimization Perspective. Foundations and Trends in Machine Learning, Boston: Now Publishers.
- Calinescu, G., Chekuri, C., Pál, M., and Vondrák, J. (2007), “Maximizing a Submodular Set Function Subject to a Matroid Constraint,” in Integer Programming and Combinatorial Optimization, Proceedings of IPCO 2007, pp. 182–196.
- Chakravarty, A. K., Orlin, J. B., and Rothblum, U. G. (1982), “A Partitioning Problem with Additive Objective with an Application to Optimal Inventory Groupings for Joint Replenishment,” Operations Research, 30, 1018–1022. DOI: 10.1287/opre.30.5.1018.
- Filmus, Y., and Ward, J. (2012), “A Tight Combinatorial Algorithm for Submodular Maximization Subject to a Matroid Constraint,” in Proceedings of the 53rd Annual IEEE Symposium on Foundations of Computer Science, pp. 659–668.
- Freige, U., Mirrokni, V. S., and Vondrak, J. (2011), “Maximizing Non-monotonic Submodular Functions,” SIAM Journal on Computing, 40, 1133–1153. DOI: 10.1137/090779346.
- Glaz, J., Naus, J., and Wallenstein, S. (2001), Scan Statistics, New York: Springer.
- Graham, R. L. (1972), “An Efficient Algorithm for Determining the Convex Hull of a Finite Planar Set,” Information Processing Letters, 1, 132–133. DOI: 10.1016/0020-0190(72)90045-2.
- Grötschel, M., Lovasz, L., and Schrijver, A. (1981), “The Ellipsoid Method and its Consequences in Combinatorial Optimization,” Combinatorica, 1, 169–197. DOI: 10.1007/BF02579273.
- Kulldorff, M. (1997), “A Spatial Scan Statistic,” Communications in Statistics: Theory and Methods, 26, 1481–1496. DOI: 10.1080/03610929708831995.
- Kulldorff, M., and Nagarwalla, N. (1995), “Spatial Disease Clusters: Detection and Inference,” Statistics in Medicine, 14, 799–810. DOI: 10.1002/sim.4780140809.
- Kulldorff, M., Fang, Z., and Walsh, S. J. (2003), “A Tree-Based Scan Statistic for Database Disease Surveillance,” Biometrics, 59, 323–331. DOI: 10.1111/1541-0420.00039.
- Lawson, A., Biggeri, A., Bohning, D., Lesare, E., Viel, J. F., and Bertollini, R., (eds.), Disease Mapping and Risk Assessment for Public Health, Chichester: Wiley.
- 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. DOI: 10.1016/j.mbs.2011.07.004.
- Naus, J. (1965a), “The Distribution of the Size of Maximum Cluster of Points on a Line,” Journal of the American Statistical Association, 60, 523–538. DOI: 10.1080/01621459.1965.10480810.
- Naus, J. (1965b), “Clustering of Random Points in Two Dimensions,” Biometrika, 52, 263–267.
- Neill, D. B. (2012), “Fast Subset Scan for Spatial Pattern Detection,” Journal of the Royal Statistical Society, Series B, 74, 337–360. DOI: 10.1111/j.1467-9868.2011.01014.x.
- Neill, D. B., Moore, A. W., and Cooper, G. F. (2006), “A Bayesian Spatial Scan Statistic,” in Advances in Neural Information Processing Systems 18, pp. 1003–1010.
- New York State Dept. of Health (2021), “New York State Cancer Registry and Cancer Statistics,” available at http://www.health.ny.gov/statistics/cancer/registry/.
- Speakman, S., McFowland, III, E., and Neill, D. B. (2015), “Scalable Detection of Anomalous Patterns with Connectivity Constraints,” Journal of Computational and Graphical Statistics, 24, 1014–1033. DOI: 10.1080/10618600.2014.960926.
- Takahashi, K., and Shimadzu, H. (2020), “Detecting Multiple Spatial Disease Clusters: Information Criterion and Scan Statistic Approach,” International Journal of Health Geographics, 19. DOI: 10.1186/s12942-020-00228-y.
- Vondrák, J. (2008), “Optimal Approximation for the Submodular Welfare Problem in the Value Oracle Model,” in Proceedings of the 40th ACM Symposium on Theory of Computing, pp. 67–74.
- Zhang, Z., Assuncao, R., and Kulldorff, M. (2010), “Spatial Scan Statistics Adjusted for Multiple Clusters,” Journal of Probability and Statistics, 10, 642379. DOI: 10.1155/2010/642379.