Scan Statistics

1. Scan Distribution Theory and its Developments

   1. Extensions of the Scan Statistic

      • Joseph Glaz, Joseph Naus, Sylvan Wallenstein

      Pages 313-332

2. Erratum

   1. Erratum to: Introduction

      • Joseph Glaz, Joseph Naus, Sylvan Wallenstein

      Pages 375-375

   2. Erratum to: Higher-Dimensional Scans

      • Joseph Glaz, Joseph Naus, Sylvan Wallenstein

      Pages 375-375

   3. Erratum to: Scanning N Uniform Distributed Points: Exact Results

      • Joseph Glaz, Joseph Naus, Sylvan Wallenstein

      Pages 375-375

   4. Erratum to: Approaches Used for Derivations and Approximations

      • Joseph Glaz, Joseph Naus, Sylvan Wallenstein

      Pages 375-375

3. Back Matter

   Pages 333-373

   PDF

In many statistical applications the scientists have to analyze the occurrence of observed clusters of events in time or space. The scientists are especially interested to determine whether an observed cluster of events has occurred by chance if it is assumed that the events are distributed independently and uniformly over time or space. Applications of scan statistics have been recorded in many areas of science and technology including: geology, geography, medicine, minefield detection, molecular biology, photography, quality control and reliability theory and radio-optics.

• Poisson process
• Random variable
• Scan Statistics
• calculus
• clustering
• statistics

From the reviews:

SHORT BOOK REVIEWS

"This is an excellent book for a graduate class or self study. The writing is extremely clear, the development is sound, and the production is of the highest quality. Of the roughly 600 references given, the authors have contributed about seven per cent, a good sign!"

"The book titled ‘Scan Statistics’ written by Glaz et al. has several statistical methodologies that are useful in bioinformatics data analysis … . is suitable for Ph.D. level course in mathematical statistics. … The bibliography … includes more than 600 references, both current and past. … I enjoyed reading ... learned a lot during the process, and in fact have raised several interesting research questions in my own mind. I strongly recommend … to statisticians, computing scientists, and genetic engineers." (Ramalingam Shanmugam, Journal of Statistical Computation and Simulation, Vol. 74 (9), September, 2004)

"The book by Glaz et al. covers scan statistics and related topics. … This book provides broad and up-to-date coverage on both approximate and exact results of scan statistics. … I enjoyed reading and learning … . I recommend … highly for statisticians and computer scientists who are interested in mastering bioinformatics and related concepts." (Ramalingam Shanmugam, Journal of Statistical Computation and Simulation, Vol. 75 (1), January, 2005)

"Scan statistics have been introduced in order to identify clusters of events in time or space. … the present book is a valuable introduction to scan statistics. It is well written … . Readers interested in the applications of scan statistics will eminently benefit … recommended to those interested in the mathematical background and the derivation of the formulas. Additionally, more than thirty pages of reference provide an excellent source for further reading and research." (Erhard Cramer, Metrika, July, 2003)

"This book gives broad andup-to-date coverage of recent developments of scan statistics, especially emphasizing exact results, approximations and bounds with a view towards applications. … Each chapter discusses in great detail the methods related to a particular scan statistic … . since the book has a lot of interesting real examples and detailed processes of derivations depending on the problems, I think it is … suitable for a graduate-level course in applied probability and statistics." (Toshiro Tango, Statistics in Medicine, Vol. 23, 2004)

"This book considers distributions of clusters of events and methods to determine if an observed cluster may be exceptional or not. … The bibliography includes over 600 references drawn from literature in diverse areas. The authors have worked in the field for decades, the second author for forty years. … Simple formulae to evaluate approximations and bounds are given for each case. … Several generalizations and extensions of scan statistics are also discussed." (Jon Stene, Mathematical Reviews, Issue 2002 m)

"The meaning of a scan statistic is clarified … . The individual chapters are devoted to exact results, approximations, and bounds for scan statistics. … The book contains a valuable bibliography that includes over 600 references. It can be recommended to researchers working in applications, as well as to specialists developing methods for the scanning of events. The material is also suitable for graduate-level courses." (EMS Newsletter, June, 2002)

"This book … does a great job of helping the novice practitioner understand the value of scan statistics. … All of the material … is surrounded by a plethora of applications. … The authors continue to illustrate the material effectively. The material is obviously much more cohesive … . This book would be a good library addition for any statistician." (Technometrics, Vol. 44 (2), 2002)

"Scan statistics are used to analyze the occurrence ofobserved clusters of events in time and space. … This book gives a broad and up-to-date coverage or exact results, approximations, and bounds for scan statistics with a view towards applications. … Both one and two-dimensional discrete and continuous scan statistics are discussed in great detail. Separate chapters are devoted to exact results, approximations, and bounds for scan statistics." (L'Enseignement Mathematique, Vol. 48 (3-4), 2002)

"This book summarizes research on scan statistics that arise naturally when analyzing the occurrence of observed clusters of events in time and space. … This book is intended for researchers in applied probability and statistics as well as for scientists who use probability models and statistical inference in their research. It is also suitable for a graduate-level course in applied probability and statistics." (Ivan Krivý, Zentralblatt MATH, Vol. 983, 2002)

• Department of Statistics The College of Liberal Arts and Sciences, University of Connecticut, Storrs, USA

  Joseph Glaz

• Department of Statistics Rutgers, The State University of New Jersey, Piscataway, USA

  Joseph Naus

• Department of Biomathematical Sciences, Mount Sinai School of Medicine, New York, USA

  Sylvan Wallenstein

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