Ebook: 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.

---

Scan statistics are used in many areas of science and technology to analyze the occurence of observed clusters of events in time and space. The goal is to determine whether an observed cluster of events occurred by chance if it is assumed that the observed events follow a specified probability model.

Scan Statistics and Applications is a comprehensive, edited survey that brings together the work of leading authorities to present the most current advances in theory and methodology for this new area of statistical research and application. The chapters contain broad coverage of theory and new analytical and computational methods and techniques in four categories: introductory survey, discrete scan statistics, continuous scan statistics, and applications.

Features and Topics:

* Comprehensive introductory survey chapter

* Discrete scan statistics

* Finite Markov chain imbedding

* Continuous scan statistics

* Spatial scan statistics

* Applications in DNA sequence analysis

* Monte Carlo approaches to testing order statistics and spacing

The book is a valuable resource and state-of-the-art reference for all practitioners, researchers, and professionals in applied probability and statistics who use scan statistics in their work.

 

---

Scan statistics are used in many areas of science and technology to analyze the occurence of observed clusters of events in time and space. The goal is to determine whether an observed cluster of events occurred by chance if it is assumed that the observed events follow a specified probability model.

Scan Statistics and Applications is a comprehensive, edited survey that brings together the work of leading authorities to present the most current advances in theory and methodology for this new area of statistical research and application. The chapters contain broad coverage of theory and new analytical and computational methods and techniques in four categories: introductory survey, discrete scan statistics, continuous scan statistics, and applications.

Features and Topics:

* Comprehensive introductory survey chapter

* Discrete scan statistics

* Finite Markov chain imbedding

* Continuous scan statistics

* Spatial scan statistics

* Applications in DNA sequence analysis

* Monte Carlo approaches to testing order statistics and spacing

The book is a valuable resource and state-of-the-art reference for all practitioners, researchers, and professionals in applied probability and statistics who use scan statistics in their work.

 

Content:
Front Matter....Pages i-xxi
Front Matter....Pages 1-1
Introduction to Scan Statistics....Pages 3-24
Front Matter....Pages 25-25
Approximations for the Distribution and the Moments of Discrete Scan Statistics....Pages 27-66
Ratchet Scan and Disjoint Statistics....Pages 67-96
Scanning Multiple Sequences....Pages 97-109
Front Matter....Pages 111-111
Approximations of the Distributions of Scan Statistics of Poisson Processes....Pages 113-139
An Approach to Computations Involving Spacings With Applications to the Scan Statistic....Pages 141-163
Using Moments to Approximate the Distribution of the Scan Statistic....Pages 165-190
Applying Ballot Problem Results to Compute Probabilities Required for a Generalization of the Scan Statistic....Pages 191-201
Scan Statistic and Multiple Scan Statistic....Pages 203-223
On Poisson Approximation for Continuous Multiple Scan Statistics in Two Dimensions....Pages 225-247
Front Matter....Pages 249-249
A Start-Up Demonstration Test Using a Simple Scan-Based Statistic....Pages 251-267
Applications of the Scan Statistic in DNA Sequence Analysis....Pages 269-286
On the Probability of Pattern Matching in Nonaligned DNA Sequences: A Finite Markov Chain Imbedding Approach....Pages 287-302
Spatial Scan Statistics: Models, Calculations, and Applications....Pages 303-322
Back Matter....Pages 323-324

---

Scan statistics are used in many areas of science and technology to analyze the occurence of observed clusters of events in time and space. The goal is to determine whether an observed cluster of events occurred by chance if it is assumed that the observed events follow a specified probability model.

Scan Statistics and Applications is a comprehensive, edited survey that brings together the work of leading authorities to present the most current advances in theory and methodology for this new area of statistical research and application. The chapters contain broad coverage of theory and new analytical and computational methods and techniques in four categories: introductory survey, discrete scan statistics, continuous scan statistics, and applications.

Features and Topics:

* Comprehensive introductory survey chapter

* Discrete scan statistics

* Finite Markov chain imbedding

* Continuous scan statistics

* Spatial scan statistics

* Applications in DNA sequence analysis

* Monte Carlo approaches to testing order statistics and spacing

The book is a valuable resource and state-of-the-art reference for all practitioners, researchers, and professionals in applied probability and statistics who use scan statistics in their work.

 

Content:
Front Matter....Pages i-xxi
Front Matter....Pages 1-1
Introduction to Scan Statistics....Pages 3-24
Front Matter....Pages 25-25
Approximations for the Distribution and the Moments of Discrete Scan Statistics....Pages 27-66
Ratchet Scan and Disjoint Statistics....Pages 67-96
Scanning Multiple Sequences....Pages 97-109
Front Matter....Pages 111-111
Approximations of the Distributions of Scan Statistics of Poisson Processes....Pages 113-139
An Approach to Computations Involving Spacings With Applications to the Scan Statistic....Pages 141-163
Using Moments to Approximate the Distribution of the Scan Statistic....Pages 165-190
Applying Ballot Problem Results to Compute Probabilities Required for a Generalization of the Scan Statistic....Pages 191-201
Scan Statistic and Multiple Scan Statistic....Pages 203-223
On Poisson Approximation for Continuous Multiple Scan Statistics in Two Dimensions....Pages 225-247
Front Matter....Pages 249-249
A Start-Up Demonstration Test Using a Simple Scan-Based Statistic....Pages 251-267
Applications of the Scan Statistic in DNA Sequence Analysis....Pages 269-286
On the Probability of Pattern Matching in Nonaligned DNA Sequences: A Finite Markov Chain Imbedding Approach....Pages 287-302
Spatial Scan Statistics: Models, Calculations, and Applications....Pages 303-322
Back Matter....Pages 323-324
....