Note: Intro -- Preface -- Contents -- Acronyms -- 1 The Problem of Simultaneous Inference -- 1.1 Sources of Multiplicity -- 1.2 Multiple Hypotheses Testing -- 1.2.1 Measuring and Controlling Errors -- 1.2.2 Structured Systems of Hypotheses -- 1.3 Relationships to Other Simultaneous Statistical Inference Problems -- 1.4 Contributions of this Work -- References -- Part IGeneral Theory -- 2 Some Theory of p-values -- 2.1 Randomized p-values -- 2.1.1 Randomized p-values in Discrete Models -- 2.1.2 Randomized p-values for Testing Composite Null Hypotheses -- 2.2 p-value Models -- 2.2.1 The iid.-Uniform Model -- 2.2.2 Dirac-Uniform Configurations -- 2.2.3 Two-Class Mixture Models -- 2.2.4 Copula Models Under Fixed Margins -- 2.2.5 Further Joint Models -- References -- 3 Classes of Multiple Test Procedures -- 3.1 Margin-Based Multiple Test Procedures -- 3.1.1 Single-Step Procedures -- 3.1.2 Stepwise Rejective Multiple Tests -- 3.1.3 Data-Adaptive Procedures -- 3.2 Multivariate Multiple Test Procedures -- 3.2.1 Resampling-Based Methods -- 3.2.2 Methods Based on Central Limit Theorems -- 3.2.3 Copula-Based Methods -- 3.3 Closed Test Procedures -- References -- 4 Simultaneous Test Procedures -- 4.1 Three Important Families of Multivariate Probability Distributions -- 4.1.1 Multivariate Normal Distributions -- 4.1.2 Multivariate t-distributions -- 4.1.3 Multivariate Chi-Square Distributions -- 4.2 Projection Methods Under Asymptotic Normality -- 4.3 Probability Bounds and Effective Numbers of Tests -- 4.3.1 Sum-Type Probability Bounds -- 4.3.2 Product-Type Probability Bounds -- 4.3.3 Effective Numbers of Tests -- 4.4 Simultaneous Test Procedures in Terms of p-value Copulae -- 4.5 Exploiting the Topological Structure of the Sample Space via Random Field Theory -- References -- 5 Stepwise Rejective Multiple Tests -- 5.1 Some Concepts of Dependency. , 5.2 FWER-Controlling Step-Down Tests -- 5.3 FWER-Controlling Step-Up Tests -- 5.4 FDR-Controlling Step-Up Tests -- 5.5 FDR-Controlling Step-Up-Down Tests -- References -- 6 Multiple Testing and Binary Classification -- 6.1 Binary Classification Under Sparsity -- 6.2 Binary Classification in Non-Sparse Models -- 6.3 Feature Selection for Binary Classification via Higher Criticism -- References -- 7 Multiple Testing and Model Selection -- 7.1 Multiple Testing for Model Selection -- 7.2 Multiple Testing and Information Criteria -- 7.3 Multiple Testing After Model Selection -- 7.3.1 Distributions of Regularized Estimators -- 7.3.2 Two-Stage Procedures -- 7.4 Selective Inference -- References -- 8 Software Solutions for Multiple Hypotheses Testing -- 8.1 The R Package multcomp -- 8.2 The R Package multtest -- 8.3 The R-based μTOSS Software -- 8.3.1 The μTOSS Simulation Tool -- 8.3.2 The μTOSS Graphical User Interface -- References -- Part IIFrom Genotype to Phenotype -- 9 Genetic Association Studies -- 9.1 Statistical Modeling and Test Statistics -- 9.2 Estimation of the Proportion of Informative Loci -- 9.3 Effective Numbers of Tests via Linkage Disequilibrium -- 9.4 Combining Effective Numbers of Tests and Pre-estimation of π0 -- 9.5 Applicability of Margin-Based Methods -- References -- 10 Gene Expression Analyses -- 10.1 Marginal Models and p-values -- 10.2 Dependency Considerations -- 10.3 Real Data Examples -- 10.3.1 Application of Generic Multiple Tests to Large-Scale Data -- 10.3.2 Copula Calibration for a Block of Correlated Genes -- 10.4 LASSO and Statistical Learning Methods -- 10.5 Gene Set Analyses and Group Structures -- References -- 11 Functional Magnetic Resonance Imaging -- 11.1 Spatial Modeling -- 11.2 False Discovery Rate Control for Grouped Hypotheses -- 11.2.1 Clusters of Voxels -- 11.2.2 Multiple Endpoints per Location. , 11.3 Exploiting Topological Structure by Random Field Theory -- 11.4 Spatio-Temporal Models via Multivariate Time Series -- 11.4.1 Which of the Specific Factors have a Non-trivial Autocorrelation Structure? -- 11.4.2 Which of the Common Factors have a Lagged Influence on Which Xi? -- References -- Part IIIFurther Applications in the Life Sciences -- 12 Further Life Science Applications -- 12.1 Brain-Computer Interfacing -- 12.2 Gel Electrophoresis-Based Proteome Analysis -- References -- Index.

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