Scan Statistics and Applications

The study of scan statistics and their applications to many different scientific and engineering problems have received considerable attention in the literature recently. In addition to challenging theoretical problems, the area of scan statis tics has also found exciting applications in diverse disciplines such as archaeol ogy, astronomy, epidemiology, geography, material science, molecular biology, reconnaissance, reliability and quality control, sociology, and telecommunica tion. This will be clearly evident when one goes through this volume. In this volume, we have brought together a collection of experts working in this area of research in order to review some of the developments that have taken place over the years and also to present their new works and point out some open problems. With this in mind, we selected authors for this volume with some having theoretical interests and others being primarily concerned with applications of scan statistics. Our sincere hope is that this volume will thus provide a comprehensive survey of all the developments in this area of research and hence will serve as a valuable source as well as reference for theoreticians and applied researchers. Graduate students interested in this area will find this volume to be particularly useful as it points out many open challenging problems that they could pursue. This volume will also be appropriate for teaching a graduate-level special course on this topic.

Auteur
Joseph Glaz has been appointed (effective July 1, 2011) as head of the Department of Statistics, University of Connecticut. He has co-authored several books. 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. N. Balakrishnan is an Associate Director and Professor at Department of Aerospace Engineering and Supercomputer Edu- cation and Research Centre, Indian Institute of Science. His research interests include numerical electromagnetic, multi-parameter radars, and signal processing. His publications include 19 books and many peer-reviewed journal papers.

Résumé

"...The subject can be quite exciting to probabilists, researchers and graduate students learning about these techniques in relation to scan statistics as a central point. The chapters are well written in a review style, discussing the main issues of scan statistics in a particular topic, and presenting the motivation and the main results, mostly without proving them. Proofs can be found in the related original papers. However, some hints and discussions are given on how to derive certain results. A few new results are scattered throughout. The book contains a useful short subject index..." -Mathematical Reviews

"The area of scan statistics is very complex with a variety of exciting theoretical results and plethora of useful applications. There are many techniques which can be used in solving problems in this area. Up to now the results were spread out in different journals. There was a need for a book consolidating the knowledge on scan statistics and providing a comprehensive survey of all the developments in this area of research. The book by Glaz and Balakrishnan achieves this and will serve as a basic reference for theoreticians and applied researchers involved or interested in scan statistics. It presents new results, describes applications of scan statistics, points out many challenging open problems for research and gives valuable references which might be of particular interest to graduate students...

To sum up, the book 'Scan Statistics and Applications,' edited by Glaz and Balakrishnan, contains excellent contributions. I enjoyed every chapter as well as the whole book. It would be interesting to have an update of the book in a few years to appreciate the developments and new results on scan statistics. The present edition of the book is good value for money." -Extremes

"...The monograph we are reviewing clearly outlines the high interest and the broad applicability of scan statisticsas a tool to analyse the occurence of observed clusters of events in time and space. 'Scan Statistics and Applications' is a comprehensive and fine edited survey that brings together results due to leading authorities in this new area of statistical research and its applications. Each chapter is closed by a rich reference list, which allows the interested reader to go deeper in one topic or another. The technical presentation of the volume is of a high level-a well-established feature of the books edited by Birkhauser Verlag in the SIT Series." -Analele Stiintifice ale Universitatii "Al.I. Cuza" Iasi

"Scan statistics have been studied and used for more than fifty years, but the present book tries to make the scattered information on this topic available in a condensed form for the first time.... The volume is a valuable source book for all researchers who are interested in the state of the art with respect to theoretical results and applications of scan statistics." -Statistics and Decisions

Contenu
I: Introduction and Preliminaries.- 1 Introduction to Scan Statistics.- II: Discrete Scan Statistics.- 2 Approximations for the Distribution and the Moments of Discrete Scan Statistics.- 3 Ratchet Scan and Disjoint Statistics.- 4 Scanning Multiple Sequences.- III: Continuous Scan Statistics.- 5 Approximations of the Distributions of Scan Statistics of Poisson Processes.- 6 An Approach to Computations Involving Spacings With Applications to the Scan Statistic.- 7 Using Moments to Approximate the Distribution of the Scan Statistic.- 8 Applying Ballot Problem Results to Compute Probabilities Required for a Generalization of the Scan Statistic.- 9 Scan Statistic and Multiple Scan Statistic.- 10 On Poisson Approximation for Continuous Multiple Scan Statistics in Two Dimensions.- IV: Applications.- 11 A Start-Up Demonstration Test Using a Simple Scan-Based Statistic.- 12 Applications of the Scan Statistic in DNA Sequence Analysis.- 13 On the Probability of Pattern Matching in Nonaligned DNA Sequences: A Finite Markov Chain Imbedding Approach.- 14 Spatial Scan Statistics: Models, Calculations, and Applications.