Handbook of Scan Statistics

ISBN-13: 9781461480327 / Angielski / Twarda / 2024 / 1400 str.

Joseph Glaz; Markos V. Koutras

Opis

The "Handbook of Scan Statistics" in two volumes is intended for researchers in probability and statistics and scientists in several areas including biology, engineering, health, medical, and social sciences. It will be of great value to graduate students in statistics and in all areas where scan statistics are used.The specialized field called 'scan statistics', fathered by Joseph Naus around 1999, burgeoned rapidly to prominence in the broader fields of applied probability and statistics. In additional to challenging theoretical problems, scan statistics has exciting applications in many areas of science and technology including archaeology, astronomy, physics, bioinformatics, and food sciences, just to name a few.In many fields, decision makers give a great deal of weight to clusters of events. Public Health investigators look for common cause factors to explain clusters of, for example, cancer. Molecular biologists look for palindrome clusters in DNA for clues as to the origin of replication viruses. Telecommunication engineers design capacity to accommodate clusters of calls being dialed simultaneously to a switchboard. Quality control experts investigate clusters of defects. The probabilities of different types of clusters under various conditions are tools of the physical, natural, and social sciences. Scan statistics arise naturally in the scanning of time and space, seeking clusters of events. It is therefore no surprise that scan statistics is a major area of research in probability and statistics in the 21st century.

Spis treści

Preface.-I. History and Early Developments.-1. Research on probability models for cluster of points before the year 1960.-2. Theoretical foundations for research in scan statistics.-3. Testing for uniformity against a clustering alternative.-4. Scan statistics for the Poisson process.-5. The Bernoulli Process and the generalized birthday problem.-II. Methods and Techniques in Research on Scan Statistics.-6. Combinatorial and exact numerical methods.-7. Generalized likelihood ratio tests.- 8. Probability inequalities.-9. Asymptotic methods.-10. Martingale methods.-11. Product-type approximations.-12. Chen-Stein Poisson and compound Poisson approximations.-13. Order Statistics.-14. Monte-Carlo and simulation algorithms.-15. Finite Markov-chain embedding methods.-16. Large deviation and saddle point approximations.-17. Bayesian models.-III. One Dimensional Scan Statistics.-18. Uniform observation in the interval (0,1).-19. Poisson process.-20. Continuous iid variables.-21. Discrete iid random variables: unconditional case.-22. Discrete iid random variables: conditional case.-23. Markov models.-24. Approximating the power of scan statistics.-25. Variable window scan statistics for Poisson processes.-26. Variable window scan statistics for iid discrete random variables.-27. Variable window scan statistics for iid continuous random variables.-28. Bayesian scan statistics.-IV. Two and Three Dimensional Scan Statistics.-29. Bernoulli trials: unconditional case.-30. Bernoulli trials: conditional case.-31. Poisson process: unconditional case.-32. Poisson process: conditional case.-33. Discrete iid random variables: conditional case.-34. Discrete iid random variables: unconditional case.-35. Continuous iid random variables.-36. Variable window scan statistics for Poisson processes.-37. Variable window scan statistics for iid discrete random variables.-38. Variable window scan statistics for iid continuous random variables.-39. Bayesian scan statistics. V. Biological Sciences.-VI. Biosurveillance and Reconnaissance.-VII. Engineering and Physical Sciences.-VIII. Ecology and Environmental Sciences.-IX. Information Sciences.-X. Medical Sciences.-XI. Public Health.-XII. Reliability and Quality Control.-XIII. Social Sciences.-XIV. Veterinary and Animal Science.

O autorze

Joseph Glaz has been recently appointed (effective July 1, 2011) as head of the Department of Statistics, University of Connecticut. He has co-authored 6 books; 4 of which published with either Birkhauser Boston or Springer New York. Glaz is the current editor-in-chief of the following Springer journal: Methodology and Computing in Applied Probability.

Honors and Awards include : election to the Connecticut Academy of Arts and Sciences (2011), elected fellow of the Institute of Mathematical Sciences (2009), AAUP Excellence in Research Award (2006), Abraham Wald Prize in Sequential Analysis (2006), elected fellow of the American Statistical Assoc. (2000), elected member of the International Statistical Institute (1999).

Most importantly, Joe Glaz has worked closely with Joseph Naus, the father of scan statistics, since this area of statistics was conceived around 1999.

Markos Koutras is currently a full professor in the department of Statistics and Actuarial Science at the University of Piraeus in Greece and served as department chair 2003-2007. He received his PhD in mathematics from the  University of Athens in 1983. Koutras serves as a highly active member of the editorial board of the Springer journal: Methodology and Computing in Applied Probability and has served on the organizing committee for several international conferences. He has served as referee/reviewer on at least 15 journals and book series. Prof. Koutras had been appointed institutional scientific director of the modernization of the central library of the University of Piraeus and director of the Graduate Program in Applied Statistics (2001-2004; 2008-2011) at Piraeus.

Blurb

The specialized field of scan statistics, fathered by Joseph Naus around 1999, burgeoned rapidly to prominence in the field of applied probability and statistics. In additional to challenging theoretical probelms, scan statistics has exciting applications in many areas of science and technologyu including archaelogy, astronomy, physics, bioinformatics, and food sciences, just to name a few.

In many fields, decision makers give a great deal of weight to clusters of events. Public Health investigators look for common cause factors to explain clusters of, for example, cancer. Molecular biologists look for palindrome clusters in DNA for clues as to the origin of replication viruses. Telecommunication engineers design capacity to accommodate clusters of calls being dialed simultaneously to a switchboard. Quality control experts investigate clusters of defects. The probabilities of different types of clusters  under various conditions are tools of the physical, natural, and social sciences. Scan statistics arise naturally in the scanning of time and space, seeking clusters of events.

It is therefore no surprise that scan statistics is a major area of research in probability and statistics in the 21st century. In the last 5 years about 1600 hits appear on Google Scholar referencing the extensive activity in scan statistics and the breadth of the application. (Since 2010, about 482 hits are recorded in Google scholar.)

The Handbook of Scan Statistics in two volumes is intended for researchers in probability and statistics and scientists in several areas including biology, engineering, health, medical, and social sciences. It will be of great value to graduate students in statistics and in all areas where scan statistics are used.