Large-scale inference : empirical Bayes methods for estimation, testing, and prediction / Bradley Efron.

Format:

Book

Author/Creator:

Efron, Bradley, author.

Contributor:

Lippincott Library Book Endowment Fund.

Series:

Institute of Mathematical Statistics monographs ; 1.

Institute of mathematical statistics monographs ; 1

Language:

English

Subjects (All):

Bayesian statistical decision theory.

Physical Description:

xii, 263 pages : illustrations (some color) ; 23 cm.

Edition:

First paperback edition.

Place of Publication:

Cambridge, UK ; New York : Cambridge University Press, 2013.

Summary:

We live in a new age for statistical inference, where modern scientific technology such as microarrays and fMRI machines routinely produce thousands and sometimes millions of parallel data sets, each with its own estimation or testing problem. Doing thousands of problems at once is more than repeated application of classical methods. Taking an empirical Bayes approach, Bradley Efron, inventor of the bootstrap, shows how information accrues across problems in a way that combines Bayesian and frequentist ideas. Estimation, testing, and prediction blend in this framework, producing opportunities for new methodologies of increased power. New difficulties also arise, easily leading to flawed inferences. This book takes a careful look at both the promise and pitfalls of large-scale statistical inference, with particular attention to false discovery rates, the most successful of the new statistical techniques. Emphasis is on the inferential ideas underlying technical developments, illustrated using a large number of real examples.

Contents:

1 Empirical Bayes and the James-Stein Estimator 1

1.1 Bayes Rule and Multivariate Normal Estimation 2

1.2 Empirical Bayes Estimation 4

1.3 Estimating the Individual Components 7

1.4 Learning from the Experience of Others 10

1.5 Empirical Bayes Confidence Intervals 12

Notes 14

2 Large-Scale Hypothesis Testing 15

2.1 A Microarray Example 15

2.2 Bayesian Approach 17

2.3 Empirical Bayes Estimates 20

2.4 Fdr(Z) as a Point Estimate 22

2.5 Independence versus Correlation 26

2.6 Learning from the Experience of Others II 27

Notes 28

3 Significance Testing Algorithms 30

3.1 p-Values and z-Values 31

3.2 Adjusted p-Values and the FWER 34

3.3 Stepwise Algorithms 37

3.4 Permutation Algorithms 39

3.5 Other Control Criteria 43

Notes 45

4 False Discovery Rate Control 46

4.1 True and False Discoveries 46

4.2 Benjamini and Hochberg's FDR Control Algorithm 48

4.3 Empirical Bayes Interpretation 52

4.4 Is FDR Control "Hypothesis Testing"? 58

4.5 Variations on the Benjamini-Hochberg Algorithm 59

4.6 Fdr and Simultaneous Tests of Correlation 64

Notes 69

5 Local False Discovery Rates 70

5.1 Estimating the Local False Discovery Rate 70

5.2 Poisson Regression Estimates for f(z) 74

5.3 Inference and Local False Discovery Rates 77

5.4 Power Diagnostics 83

Notes 88

6 Theoretical, Permutation, and Empirical Null Distributions 89

6.1 Four Examples 90

6.2 Empirical Null Estimation 97

6.3 The MLE Method for Empirical Null Estimation 102

6.4 Why the Theoretical Null May Fail 105

6.5 Permutation Null Distributions 109

Notes 112

7 Estimation Accuracy 113

7.1 Exact Covariance Formulas 115

7.2 Rms Approximations 121

7.3 Accuracy Calculations for General Statistics 126

7.4 The Non-Null Distribution of z-Values 132

7.5 Bootstrap Methods 138

Notes 139

8 Correlation Questions 141

8.1 Row and Column Correlations 141

8.2 Estimating the Root Mean Square Correlation 145

8.3 Are a Set of Microarrays Independent of Each Other? 149

8.4 Multivariate Normal Calculations 153

8.5 Count Correlations 159

Notes 162

9 Sets of Cases (Enrichment) 163

9.1 Randomization and Permutation 164

9.2 Efficient Choice of a Scoring Function 170

9.3 A Correlation Model 174

9.4 Local Averaging 181

Notes 184

10 Combination, Relevance, and Comparability 185

10.1 The Multi-Class Model 187

10.2 Small Subclasses and Enrichment 192

10.3 Relevance 196

10.4 Are Separate Analyses Legitimate? 199

10.5 Comparability 206

Notes 209

11 Prediction and Effect Size Estimation 211

11.1 A Simple Model 213

11.2 Bayes and Empirical Bayes Prediction Rules 217

11.3 Prediction and Local False Discovery Rates 223

11.4 Effect Size Estimation 227

11.5 The Missing Species Problem 233

Notes 240.

Notes:

Includes bibliographical references (pages 251-257) and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Lippincott Library Book Endowment Fund.

ISBN:

9781107619678

110761967X

9780521192491

0521192498

OCLC:

809937900