Handbook of Scan Statistics von Joseph Glaz/Markos V Koutras

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.

InhaltsangabePreface.-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.