Scan Statistics and Applications

"...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 statistics as 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

• 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.