Glaz / Pozdnyakov / Wallenstein Scan Statistics

Methods and Applications
1. Auflage 2009
ISBN: 978-0-8176-4749-0
Verlag: Birkhäuser Boston
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 394 Seiten

Reihe: Statistics for Industry and Technology

Scan statistics is currently one of the most active and important areas of research in applied probability and statistics, having applications to a wide variety of fields: archaeology, astronomy, bioinformatics, biosurveillance, molecular biology, genetics, computer science, electrical engineering, geography, material sciences, physics, reconnaissance, reliability and quality control, telecommunication, and epidemiology. Filling a gap in the literature, this self-contained volume brings together a collection of selected chapters illustrating the depth and diversity of theory, methods and applications in the area of scan statistics.

Autoren/Hrsg.

Glaz, Joseph

Pozdnyakov, Vladimir

Wallenstein, Sylvan

Inhaltsverzeichnis

1;Contents;7
2;Preface;15
3;Contributors;17
4;List of Tables;20
5;List of Figures;23
6;Joseph Naus: Father of the Scan Statistic;27
6.1;1.1 Naus (1963): Ph.D. Thesis;28
6.2;1.2 The Early Papers Touching All Aspects of the Problem: 1965– 1968;31
6.3;1.3 Joseph Naus’s Students in 1967–1978, Exploitation of Ballot Problem Results, Broadening of Problem;35
6.4;1.4 Two Key Publications, 1979–1982;40
6.5;1.5 Later Work, Briefly Noted;42
6.6;References;46
7;Precedence-Type Tests for the Comparison of Treatments with a Control;52
7.1;2.1 Introduction;52
7.2;2.2 Review of Precedence-Type Tests;54
7.3;2.3 Test Statistics for Comparing k 1 Treatments with Control;58
7.4;2.4 Exact Power Under Lehmann Alternative;66
7.5;2.5 Discussion;67
7.6;2.6 Illustrative Example;69
7.7;Appendix A: Probability Mass Function of (M2, . . . , Mk ) Under the Null Hypothesis;70
7.8;Appendix B: Probability Mass Function of (M2, . . . , Mk ) Under the Lehmann Alternative;73
7.9;References;78
8;Extreme Value Results for Scan Statistics;80
8.1;3.1 Introduction;80
8.2;3.2 Definitions and Notation;82
8.3;3.3 The Binary Scan Statistic;85
8.4;3.4 Scan Statistic Exceedances;96
8.5;References;109
9;Boundary Crossing Probability Computations in the Analysis of Scan Statistics;111
9.1;4.1 Introduction;111
9.2;4.2 Theoretical Developments;112
9.3;4.3 Applications in Spatial Scan Statistics;116
9.4;4.4 Recent Applications in Genomics;121
9.5;4.5 Concluding Remarks;127
9.6;References;128
10;Approximations for Two-Dimensional Variable Window Scan Statistics;133
10.1;5.1 Introduction;133
10.2;5.2 Two-Dimensional Discrete Scan Statistics;134
10.3;5.3 Variable Window Discrete-Type Scan Statistics;141
10.4;5.4 Numerical Results;145
10.5;5.5 Summary;149
10.6;References;150
11;Applications of Spatial Scan Statistics: A Review;153
11.1;6.1 Introduction;153
11.2;6.2 Brief Methodological Overview;154
11.3;6.3 Applications in Medical Imaging;156
11.4;6.4 Applications in Cancer Epidemiology;156
11.5;6.5 Applications in Infectious Disease Epidemiology;158
11.6;6.6 Applications in Parasitology;160
11.7;6.7 Other Medical Applications;161
11.8;6.8 Applications in Veterinary Medicine;162
11.9;6.9 Applications in Forestry;162
11.10;6.10 Applications in Geology;163
11.11;6.11 Applications in Astronomy;163
11.12;6.12 Applications in Psychology;164
11.13;6.13 Applications to Accidents;164
11.14;6.14 Applications in Criminology and Warfare;164
11.15;6.15 Applications in Demography;165
11.16;6.16 Applications in the Humanities;165
11.17;6.17 Scan Statistic Software;165
11.18;6.18 Discussion;166
11.19;References;166
12;Extensions of the Scan Statistic for the Detection and Inference of Spatial Clusters;177
12.1;7.1 Introduction;177
12.2;7.2 Irregularly Shaped Spatial Clusters;178
12.3;7.3 Data-Driven Spatial Cluster Detection Models;187
12.4;7.4 Applications;191
12.5;References;191
13;1-Dependent Stationary Sequences and Applications to Scan Statistics;202
13.1;8.1 Introduction;202
13.2;8.2 Application of the Approximations (8.6) and ( 8.7) to One- Dimensional Scan Statistics;207
13.3;8.3 Application of the Method to Two-Dimensional Scan Statistics;211
13.4;References;214
14;Scan Statistics in Genome-Wide Scan for Complex Trait Loci;217
14.1;9.1 Introduction;217
14.2;9.2 Methods;218
14.3;9.3 Applications;219
14.4;9.4 Discussion;221
14.5;References;222
15;On Probabilities for Complex Switching Rules in Sampling Inspection;225
15.1;10.1 Introduction;225
15.2;10.2 Notation and Finite Markov Chain Imbedding;227
15.3;10.3 Main Results;228
15.4;10.4 Numerical Examples of Switching Rules;232
15.5;10.5 Summary and Discussion;238
15.6;References;240
16;Bayesian Network Scan Statistics for Multivariate Pattern Detection;242
16.1;11.1 Introduction;242
16.2;11.2 The Multivariate Bayesian Scan Statistic;249
16.3;11.3 The Agent-Based Bayesian Scan Statistic;256
16.4;11.4 The Anomalous Group Detection Method;261
16.5;References;267
17;ULS Scan Statistic for Hotspot Detection with Continuous Gamma Response;271
17.1;12.1 Introduction;272
17.2;12.2 Basic Ideas;273
17.3;12.3 ULS Scan Statistic;274
17.4;12.4 Computational Aspects;276
17.5;12.5 Testing Significance of the Scan Statistic;278
17.6;12.6 Gamma Response Model;278
17.7;12.7 Details of Software Implementation;280
17.8;12.8 Construction of the ULS Scan Tree;283
17.9;12.9 A Case Study;285
17.10;12.10 Conclusions;287
17.11;References;288
18;False Discovery Control for Scan Clustering;291
18.1;13.1 Introduction;291
18.2;13.2 The Basics of Multiple Testing;292
18.3;13.3 The Method;294
18.4;13.4 Clusters Shaving for Bias Correction;298
18.5;13.5 Power Increase Through Multiple Bandwidths;300
18.6;13.6 Examples;301
18.7;References;306
19;Martingale Methods for Patterns and Scan Statistics;308
19.1;14.1 Introduction;308
19.2;14.2 Patterns in an Independent Sequence;309
19.3;14.3 Compound Patterns and Gambling Teams;313
19.4;14.4 Patterns in Markov Dependent Trials;318
19.5;14.5 Applications to Scans;327
19.6;14.6 Concluding Remarks;335
19.7;References;335
20;How Can Pattern Statistics Be Useful for DNA Motif Discovery?;337
20.1;15.1 Introduction;337
20.2;15.2 Words with Exceptional Frequency;338
20.3;15.3 Words with Exceptional Distribution;357
20.4;15.4 More Sophisticated Patterns;360
20.5;15.5 Ongoing Research and Open Problems;364
20.6;References;365
21;Occurrence of Patterns and Motifs in Random Strings;369
21.1;16.1 Introduction;369
21.2;16.2 Patterns: Discrete-Time Models;371
21.3;16.3 Patterns: General Discrete-Time and Continuous- Time Models;374
21.4;16.4 Compound Patterns;377
21.5;References;382
22;Detection of Disease Clustering;386
22.1;17.1 Introduction;386
22.2;17.2 Temporal Clustering;387
22.3;17.3 Spatial Clustering;394
22.4;17.4 Discussion;403
22.5;References;405
23;Index;409