Scan Statistics

Scan statistics are used extensively in many areas of science and technology to analyze the occurrence of observed clusters of events in time and space. Scientists seek to determine whether an observed cluster of events has occurred by chance or if it signals a departure from the underlying probability model for the observed data. This book gives broad and up-to-date coverage or exact results, approximations, and bounds for scan statistics with a view towards applications. A special feature of the book is its division in two parts. The first part consists of six chapters and is focused on the use of scan statistics in applications. Each chapter discusses in great detail the methods related to a particular scan statistic, applying them to the areas of astronomy, medicine, molecular biology, and quality control. Simple formulae to evaluate approximations and bounds are given for each case. Most of these formulae can be implemented with the use of a calculator and readily available statistical tables. The second part of the book consists of twelve chapters and presents the development of the theory and methods of scan statistics. Both one- and two-dimensional discrete and continuous scan statistics are discussed in great detail. Separate chapters are devoted to exact results, approximations, and bounds for scan statistics. Additional chapters on the power of scan statistics and its generalizations to accommodate applications when the size of the sliding window is unknown or there is a need to detect clustering of events superimposed on temporal or seasonal trends are included as well. Scan Statistics will be of interest to researchers in applied probability and statistics and scientists who use probability models and statistical inference in their research. The bibliography includes over 600 references drawn from literature in diverse areas. The book is suitable for a graduate-level course in applied probability and statistics.