Handbook of Scan Statistics, 1st ed. 2024

Scan statistics, one of the most active research areas in applied probability and statistics, has seen a tremendous growth during the last 25 years. Google Scholar lists about 3,500 hits to references of articles on scan statistics since the year 2020, resulting in over 850 hits to articles per year. This is mainly due to extensive and diverse areas of science and technology where scan statistics have been employed, including: atmospheric and climate sciences, business, computer science, criminology, ecology, epidemiology, finance, genetics and genomics, geographic sciences, medical and health sciences, nutrition, pharmaceutical sciences, physics, quality control and reliability, social networks and veterinary science.

                This volume of the Handbook of Scan Statistics is a collection of forty chapters, authored by leading experts in the field, outlines the research and the breadth of applications of scan statistics to  the numerous areas of science and technology listed above. These chapters present an overview of the theory, methods and computational techniques, related to research in the area of scan statistics and outline future developments. It contains extensive references to research articles, books and relevant computer software.

               Handbook of Scan Statistics is an excellent reference for researchers and graduate students in applied probability and statistics, as well as for scientists in research areas where scan statistics are used. This volume may also be used as a textbook for a graduate level course on scan statistics. 

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

 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

26. Variable window scan statistics for iid discrete random variables

27. Variable window scan statistics for iid continuous random variables

28. Bayesian 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

38. Variable window scan statistics for iid continuous random variables

39. Bayesian scan statistics. V. Biological Sciences

VI. Biosurveillance and Reconnaissance

VIII. Ecology and Environmental Sciences

IX. Information Sciences

X. Medical Sciences

XI. Public Health

XIII. Social Sciences

XIV. Veterinary and Animal Science.

Joseph Glaz is Professor, Department of Statistics, University of Connecticut, where he served as Department Head in 2011-2016. He received his Ph. D. in Statistics from Rutgers University in 1978. Areas of research interest include: geometrical probability, parametric bootstrap, scan statistics, sequential analysis and simultaneous inference. He was elected Ordinary Member of the International Statistical Institute in 1996, Fellow of American Statistical Association in 2000, Fellow of the Institute of Mathematical Statistics in 2009 and to Connecticut Academy of Arts and Sciences in 2011. He is a recipient of Abraham Wald Prize in Sequential Analysis in 2006 and the AAUP Excellence in Research Award in 2008. He is a founding Editor, and serving since 1998 as Editor in chief, of a scientific journal Methodology and Computing in Applied Probability, published currently by Springer Nature.

Markos V. Koutras is Professor in the Department of Statistics and Insurance Science, University of Piraeus, Greece. He served as Department Head, Dean and MSc director (MSc program in Biostatistics and MSc program in Applied Statistics) for several years as well as Vice Rector for the University of Piraeus in 2017-2022.

He received his B.S. in Mathematics (1979) and holds an MSc in Computer Science and Operations Research (1981) and a PhD in Statistics (1983). His research interests include, among others, theory of run and scan statistics, statistical process control, reliability theory and multivariate statistical analysis. He has more than 100 publications in referred Journals and 20 publications in referred special volumes (by invitation). He serves as Associate Editor in 8 international journals, he has been guest Editor in 6 special issues for international journals and he was recently appointed co-Editor in Chief in Methodology and Computing in Applied Probability, published by Springer Nature. He has authored/co-authored

Reference for grad students in applied probability and scientists in applied areas where scan statistics is used

Theoretical and methodological advances in the area of scan statistics and its applications

40 chapters in this volume are authored by leading experts in the field