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E-raamat: Simultaneous Statistical Inference: With Applications in the Life Sciences

  • Formaat: PDF+DRM
  • Ilmumisaeg: 23-Jan-2014
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Keel: eng
  • ISBN-13: 9783642451829
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Simultaneous Statistical Inference: With Applications in the Life SciencesSuurem pilt
  • Formaat: PDF+DRM
  • Ilmumisaeg: 23-Jan-2014
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Keel: eng
  • ISBN-13: 9783642451829
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This monograph offers an in-depth mathematical treatment of modern multiple test procedures controlling the false discovery rate and related error measures, particularly addressing applications to such fields as genetics, proteomics and neuroscience.

This monograph will provide an in-depth mathematical treatment of modern multiple test procedures controlling the false discovery rate (FDR) and related error measures, particularly addressing applications to fields such as genetics, proteomics, neuroscience and general biology. The book will also include a detailed description how to implement these methods in practice. Moreover new developments focusing on non-standard assumptions are also included, especially multiple tests for discrete data. The book primarily addresses researchers and practitioners but will also be beneficial for graduate students.

Arvustused

Thorsten Dickhaus Simultaneous Statistical Inference is without a doubt the most thorough yet concise roundup of multiple-test procedures that has come out in many years. It is all the more worthwhile reading for statistical researchers, who will be guided through the maze of multiple-testing approaches that have accumulated over the past decades. a rich source of inspiration for anyone who has some mathematical background and seeks a deep understanding of state-of-the-art simultaneous inference. (Philip Pallmann, Biometrical Journal, Vol. 57 (6), 2015)

1 The Problem of Simultaneous Inference
1(16)
1.1 Sources of Multiplicity
3(1)
1.2 Multiple Hypotheses Testing
4(5)
1.2.1 Measuring and Controlling Errors
4(4)
1.2.2 Structured Systems of Hypotheses
8(1)
1.3 Relationships to Other Simultaneous Statistical Inference Problems
9(2)
1.4 Contributions of this Work
11(6)
References
12(5)
Part I General Theory
2 Some Theory of p-values
17(12)
2.1 Randomized p-values
20(2)
2.1.1 Randomized p-values in Discrete Models
20(1)
2.1.2 Randomized p-values for Testing Composite Null Hypotheses
21(1)
2.2 p-value Models
22(7)
2.2.1 The iid.-Uniform Model
22(2)
2.2.2 Dirac-Uniform Configurations
24(1)
2.2.3 Two-Class Mixture Models
25(1)
2.2.4 Copula Models Under Fixed Margins
26(1)
2.2.5 Further Joint Models
26(1)
References
27(2)
3 Classes of Multiple Test Procedures
29(18)
3.1 Margin-Based Multiple Test Procedures
30(7)
3.1.1 Single-Step Procedures
30(2)
3.1.2 Stepwise Rejective Multiple Tests
32(3)
3.1.3 Data-Adaptive Procedures
35(2)
3.2 Multivariate Multiple Test Procedures
37(3)
3.2.1 Resampling-Based Methods
37(1)
3.2.2 Methods Based on Central Limit Theorems
38(1)
3.2.3 Copula-Based Methods
38(2)
3.3 Closed Test Procedures
40(7)
References
43(4)
4 Simultaneous Test Procedures
47(24)
4.1 Three Important Families of Multivariate Probability Distributions
50(2)
4.1.1 Multivariate Normal Distributions
50(1)
4.1.2 Multivariate t-distributions
51(1)
4.1.3 Multivariate Chi-Square Distributions
51(1)
4.2 Projection Methods Under Asymptotic Normality
52(4)
4.3 Probability Bounds and Effective Numbers of Tests
56(6)
4.3.1 Sum-Type Probability Bounds
57(1)
4.3.2 Product-Type Probability Bounds
58(3)
4.3.3 Effective Numbers of Tests
61(1)
4.4 Simultaneous Test Procedures in Terms of p-value Copulae
62(3)
4.5 Exploiting the Topological Structure of the Sample Space via Random Field Theory
65(6)
References
68(3)
5 Stepwise Rejective Multiple Tests
71(20)
5.1 Some Concepts of Dependency
72(2)
5.2 FWER-Controlling Step-Down Tests
74(2)
5.3 FWER-Controlling Step-Up Tests
76(4)
5.4 FDR-Controlling Step-Up Tests
80(2)
5.5 FDR-Controlling Step-Up-Down Tests
82(9)
References
89(2)
6 Multiple Testing and Binary Classification
91(12)
6.1 Binary Classification Under Sparsity
93(3)
6.2 Binary Classification in Non-Sparse Models
96(3)
6.3 Feature Selection for Binary Classification via Higher Criticism
99(4)
References
101(2)
7 Multiple Testing and Model Selection
103(14)
7.1 Multiple Testing for Model Selection
104(2)
7.2 Multiple Testing and Information Criteria
106(2)
7.3 Multiple Testing After Model Selection
108(4)
7.3.1 Distributions of Regularized Estimators
108(3)
7.3.2 Two-Stage Procedures
111(1)
7.4 Selective Inference
112(5)
References
114(3)
8 Software Solutions for Multiple Hypotheses Testing
117(12)
8.1 The R Package multcomp
118(1)
8.2 The R Package multtest
118(1)
8.3 The R-based μTOSS Software
119(10)
8.3.1 The μTOSS Simulation Tool
120(2)
8.3.2 The μTOSS Graphical User Interface
122(2)
References
124(5)
Part II From Genotype to Phenotype
9 Genetic Association Studies
129(12)
9.1 Statistical Modeling and Test Statistics
130(3)
9.2 Estimation of the Proportion of Informative Loci
133(1)
9.3 Effective Numbers of Tests via Linkage Disequilibrium
134(3)
9.4 Combining Effective Numbers of Tests and Pre-estimation of π0
137(1)
9.5 Applicability of Margin-Based Methods
138(3)
References
139(2)
10 Gene Expression Analyses
141(14)
10.1 Marginal Models and p-values
141(2)
10.2 Dependency Considerations
143(3)
10.3 Real Data Examples
146(3)
10.3.1 Application of Generic Multiple Tests to Large-Scale Data
146(1)
10.3.2 Copula Calibration for a Block of Correlated Genes
147(2)
10.4 LASSO and Statistical Learning Methods
149(1)
10.5 Gene Set Analyses and Group Structures
150(5)
References
151(4)
11 Functional Magnetic Resonance Imaging
155(14)
11.1 Spatial Modeling
156(1)
11.2 False Discovery Rate Control for Grouped Hypotheses
157(3)
11.2.1 Clusters of Voxels
157(2)
11.2.2 Multiple Endpoints per Location
159(1)
11.3 Exploiting Topological Structure by Random Field Theory
160(1)
11.4 Spatio-Temporal Models via Multivariate Time Series
161(8)
11.4.1 Which of the Specific Factors have a Non-trivial Autocorrelation Structure?
164(1)
11.4.2 Which of the Common Factors have a Lagged Influence on Which Xi?
165(1)
References
165(4)
Part III Further Applications in the Life Sciences
12 Further Life Science Applications
169(8)
12.1 Brain-Computer Interfacing
169(3)
12.2 Gel Electrophoresis-Based Proteome Analysis
172(5)
References
174(3)
Index 177
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