Scan Statistics

In many statistical applications the scientists have to analyze the occurrence of observed clusters of events in time or space. The scientists are especially interested to determine whether an observed cluster of events has occurred by chance if it is assumed that the events are distributed independently and uniformly over time or space. Applications of scan statistics have been recorded in many areas of science and technology including: geology, geography, medicine, minefield detection, molecular biology, photography, quality control and reliability theory and radio-optics.

I Methods and Applications.- 1 Introduction.- 2 Retrospective Scanning of Events Over Time.- 3 Prospective Scanning of Events Over Time.- 4 Success Scans in a Sequence of Trials.- 5 Higher-Dimensional Scans.- 6 Scan Statistics in DNA and Protein Sequence Analysis.- II Scan Distribution Theory and its Developments.- 7 Approaches Used for Derivations and Approximations.- 8 Scanning N Uniform Distributed Points: Exact Results.- 9 Scanning N Uniform Distributed Points: Bounds.- 10 Approximations for the Conditional Case.- 11 Scanning Points in a Poisson Process.- 12 The Generalized Birthday Problem.- 13 Scan Statistics for a Sequence of Discrete I.I.D. Variates.- 14 Power.- 15 Testing for Clustering.- 16 Two-Dimensional Scan Statistics.- 17 Number of Clusters: Ordered Spacings.- 18 Extensions of the Scan Statistic.- References.