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ULS Scan Statistic for Hotspot Detection with Continuous Gamma Response

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Scan Statistics

Part of the book series: Statistics for Industry and Technology ((SIT))

Abstract

An approach using the upper level set (ULS) scan statistic to detect geospatial hotspots along with its software implementation is presented for continuous response. The ULS scan statistic is based on the ULS scan tree. A ULS scan tree is a data structure constructed from response data over a geographic region partitioned into cells. Candidates for hotspots are zones in the region. Each such candidate zone consists of cells that are connected geographically. A ULS scan tree is used to identify candidate zones systematically. Nodes of the ULS scan tree are connected zones. The root (the bottom level) of the ULS scan tree is a zone consisting of the entire region. Zones at the top level (leaf zones) consist of cells with maximal response values. For in-between levels, zones at a given level consist of connected cells with higher response values than zones at a lower level. A suitable likelihood statistic and Monte Carlo analysis are used to determine the significance of zonal nodes as hotspots. The gamma response model is studied in detail. A case study illustrating application of the gamma response model is presented.

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References

  1. Biomedware (2001). Software for the Environmental and Health Sciences, Biomedware, Ann Arbor, MI.

    Google Scholar 

  2. Cressie, N. (1991). Statistics for Spatial Data, John Wiley & Sons, New York.

    MATH  Google Scholar 

  3. Glaz, J., and Balakrishnan, N. (1999). Scan Statistics and Applications, Springer Publications, Netherlands.

    MATH  Google Scholar 

  4. Glaz, J., Naus, J., and Wallenstein, S. (2001). Scan Statistics, Springer Publications, New York.

    MATH  Google Scholar 

  5. Joly, K. (1996). Mammalian biodiversity in Pennsylvania at the USEPA 635 square kilometer hexagonal scale, Master of Science thesis, Pennsylvania State University, University Park, PA.

    Google Scholar 

  6. Kulldorff, M. (1997). A spatial scan statistic, Communications in Statistics: Theory and Methods, 26(6), 1481–1496.

    Article  MATH  MathSciNet  Google Scholar 

  7. Kulldorff, M. (2006). SaTScan v 7.0: Software for the spatial and space-time scan statistics, Information Management Services Inc., Silver Spring, MD.

    Google Scholar 

  8. Kulldorff, M., and Nagarwala, N. (1995). Spatial disease clusters: detection and inference, Statistics in Medicine, 14, 799–810.

    Article  Google Scholar 

  9. Kulldorff, M., Rand, K., Gherman, G., Williams, G., and DeFrancesco, D. (1998). SaTScan v 2.1: Software for the spatial and space-time scan statistics, National Cancer Institute, Bethesda, MD.

    Google Scholar 

  10. Myers, W., Bishop, J., Brooks, R., O’Connell, T., Argent, D., Storm, G., Stauffer, J., and Carline, R. (2000). Pennsylvania Gap Analysis Project; leading landscapes for collaborative conservation: Final report. School of Forest Resources, Cooperative Fish and Wildlife Research Unit, and Environmental Resources Research Institute. Pennsylvania State University, University Park, PA.

    Google Scholar 

  11. Patil, G.P. (2007). Statistical geoinformatics of geographic hotspot detection and multicriteria prioritization for monitoring, etiology, early warning and sustainable management for digital governance in agriculture, environment, and ecohealth, Journal of Indian Society of Agricultural Statistics, 61, 132–146.

    MathSciNet  Google Scholar 

  12. Patil, G.P., and Taillie, C. (2003). Geographic and network surveillance via scan statistics for critical area detection, Statistical Science, 18(4), 457–465.

    Article  MATH  MathSciNet  Google Scholar 

  13. Patil, G.P., and Taillie, C. (2004). Upper level set scan statistic for detecting arbitrarily shaped hotspots. Environmental Ecological Statistics, 11, 183–197.

    Article  MathSciNet  Google Scholar 

  14. Patil, G.P., Acharya, R., Glasmier, A., Myers, W., Phoha, S., and Rathbun, S. (2006). Hotspot detection and prioritization geoinformatics for digital governance, In Digital Government: Advanced Research and Case Studies (Eds., H. Chen, L. Brandt, V. Gregg, R. Traunmüller, S. Dawes, E. Hovy, A. Macintosh, C. Larson), Springer, New York.

    Google Scholar 

  15. Patil, G.P., Acharya, R., Myers, W., Phoha, S., and Zambre, R. (2007). Hotspot geoinformatics for detection, prioritization, and security, In Encyclopedia of Geographical Information Science (Eds., S. Shekhar and H. Xiong), Springer, New York.

    Google Scholar 

  16. Patil, G.P., Acharya, R., and Phoha, S. (2007). Digital governance, hotspot detection, and homeland security, In Encyclopedia of Quantitative Risk Analysis, Wiley, New York.

    Google Scholar 

  17. Patil, G.P., Acharya, R., Modarres, R., Myers, W.L., and Rathbun, S.L. (2007). Hotspot geoinformatics for digital government. In Encyclopedia of Digital Government, Volume II (Eds. Ari-Veikko Anttiroiko and Matti Malkia), Idea Group Publishing, Hershey, PA, 919.

    Google Scholar 

  18. Patil, G.P., Joshi, S.W., and Rathbun, S.L. (2007). Hotspot geoinformatics, environmental risk, and digital governance, In Encyclopedia of Quantitative Risk Analysis, Wiley, New York.–927, Idea Group Reference, Hershey, PA.

    Google Scholar 

  19. Patil, G.P., Patil, V.D., Pawde, S.P., Phoha, S., Singhal, V., and Zambre, R. (2008). Digital governance, hotspot geoinformatics, and sensor networks for monitoring, etiology, early warning, and sustainable management, In Geoinformatics for Natural Resource Management (Ed. P.K. Joshi), Nova Science Publishers, New York (in press).

    Google Scholar 

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Acknowledgements

The first author acknowledges that this material is based upon work supported by (1) The National Science Foundation under Grant No. 0307010, and (ii) The United States Environmental Protection Agency under Grant No. CR-83059301 and No. R-828684-01. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the agencies.

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Authors and Affiliations

  1. Department of Statistics, Center for Statistical Ecology and Environmental Statistics, The Pennsylvania State University, University Park, PA, USA

    Ganapati P. Patil

  2. School of Forest Resources, The Pennsylvania State University, University Park, PA, USA

    Wayne L. Myers

  3. Watershed Surveillance and Research Institute, JalaSRI, M.J. College, Jalgaon, India

    Rajesh E. Koli

Authors
  1. Ganapati P. Patil
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  2. Sharadchandra W. Joshi
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  3. Wayne L. Myers
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  4. Rajesh E. Koli
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Editor information

Editors and Affiliations

  1. Dept. Statistics, University of Connecticut, Glenbrook Rd. 215, Storrs, 06269-3120, U.S.A.

    Joseph Glaz

  2. Dept. Statistics, University of Connecticut, Glenbrook Road 215, Storrs, 06269-4120, U.S.A.

    Vladimir Pozdnyakov

  3. Center for Biomathematical Sciences, Mount Sinai School of Medicine, Gustave L Levy Place 1, New York, 10029, U.S.A.

    Sylvan Wallenstein

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© 2009 Birkhäuser Boston, a part of Springer Science+Business Media, LLC

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Patil, G.P., Joshi, S.W., Myers, W.L., Koli, R.E. (2009). ULS Scan Statistic for Hotspot Detection with Continuous Gamma Response. In: Glaz, J., Pozdnyakov, V., Wallenstein, S. (eds) Scan Statistics. Statistics for Industry and Technology. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4749-0_12

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