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.

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Preface Contributors List of Tables List of Figures Part I. Introduction and Preliminaries Introduction to Scan Statistics \ Joseph Glaz and N. Balakrishnan Part II. Discrete Scan Statistics Approximations for the Distribution and the Moments of Discrete Scan Statistics \ Jie Chen and Joseph Glaz Ratchet Scan adn Disjoint Statistics \ Joachim Krauth Scanning Multiple Sequences \ Joseph I. Naus Part III. Continuous Scan Statistics Approximations of the Distributions of Scan Statistics of Poisson Processes \ Sve Erick Alm An Approach to Computations Involving Spacings With Applications to the Scan Statistic \ Fred W. Huffer and Chien-Tai Lin Using Moments to Approximate the Distribution of the Scan Statistic \ Fred W. Huffer and Chien-Tai Lin Applying Ballot Problem Results to Compute Probabilities Required for a Generalization of the Scan Statistic \ Sylvan Wallenstein Scan Statistic and Multiple Scan Statistic \ Chien-Tai Lin On Poisson Approximation for Continuous Multiple Scan Statistics in Two Dimensions \ Marianne Månsson Part IV. Applications A Start-Up Demonstration Test Using a Simple Scan-Based Statistic \ Markos V. Koutras and N. Balakrishnan Applications of the Scan Statistic in DNA Sequence Analysis \ Ming-Ying Leung and Traci E. Yamashita On the Probability of Pattern Matching in Nonaligned DNA Sequences: A Finite Markov Chain Imbedding Approach \ James C. Fu, W.Y. Wendy Lou, and S.C. Chen Spacial Scan Statistics: Models, Calculations, and Applications \ Martin Kulldorff Index