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Author Efron, Bradley.

Title Large-scale inference : empirical Bayes methods for estimation, testing, and prediction / Bradley Efron
Published Cambridge ; New York : Cambridge University Press, [2010]
©2010
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Description 1 online resource (xii, 263 pages) : illustrations
Series Institute of mathematical statistics monographs ; 1
Institute of Mathematical Statistics monographs ; 1
Contents Prologue -- Acknowledgments -- 1 Empirical Bayes and the James-Stein Estimator -- 1.1 Bayes Rule and Multivariate Normal Estimation -- 1.2 Empirical Bayes Estimation -- 1.3 Estimating the Individual Components -- 1.4 Learning from the Experience of Others -- 1.5 Empirical Bayes Confidence Intervals -- Notes -- 2 Large-Scale Hypothesis Testing -- 2.1 A Microarray Example -- 2.2 Bayesian Approach -- 2.3 Empirical Bayes Estimates -- 2.4 Fdr(Z) as a Point Estimate -- 2.5 Independence versus Correlation -- 2.6 Learning from the Experience of Others II -- Notes -- 3 Significance Testing Algorithms -- 3.1 p-Values and z-Values -- 3.2 Adjusted p-Values and the FWER -- 3.3 Stepwise Algorithms -- 3.4 Permutation Algorithms -- 3.5 Other Control Criteria -- Notes -- 4 False Discovery Rate Control -- 4.1 True and False Discoveries -- 4.2 Benjamini and Hochberg's FDR Control Algorithm -- 4.3 Empirical Bayes Interpretation -- 4.4 Is FDR Control"Hypothesis Testing"? -- 4.5 Variations on the Benjamini-Hochberg Algorithm -- 4.6 Fdr and Simultaneous Tests of Correlation -- Notes -- 5 Local False Discovery Rates -- 5.1 Estimating the Local False Discovery Rate -- 5.2 Poisson Regression Estimates for f (z) -- 5.3 Inference and Local False Discovery Rates -- 5.4 Power Diagnostics -- Notes -- 6 Theoretical, Permutation, and Empirical Null Distributions -- 6.1 Four Examples -- A. Leukemia study -- B. Chi-square data -- C. Police data -- D. HIV data -- 6.2 Empirical Null Estimation -- 6.3 The MLE Method for Empirical Null Estimation -- 6.4 Why the Theoretical Null May Fail -- 6.5 Permutation Null Distributions -- Notes -- 7 Estimation Accuracy -- 7.1 Exact Covariance Formulas -- 7.2 Rms Approximations -- 7.3 Accuracy Calculations for General Statistics -- 7.4 The Non-Null Distribution of z-Values -- 7.5 Bootstrap Methods -- Notes -- 8 Correlation Questions -- 8.1 Row and Column Correlations -- Standardization -- 8.2 Estimating the Root Mean Square Correlation -- Simulating correlated z-values -- 8.3 Are a Set of Microarrays Independent of Each Other? -- 8.4 Multivariate Normal Calculations -- Effective sample size -- Correlation of t-values -- 8.5 Count Correlations -- Notes -- 9 Sets of Cases (Enrichment) -- 9.1 Randomization and Permutation -- 9.2 Efficient Choice of a Scoring Function -- 9.3 A Correlation Model -- 9.4 Local Averaging -- Notes -- 10 Combination, Relevance, and Comparability -- 10.1 The Multi-Class Model -- 10.2 Small Subclasses and Enrichment -- Enrichment -- Efficiency -- 10.3 Relevance -- 10.4 Are Separate Analyses Legitimate? -- 10.5 Comparability -- Notes -- 11 Prediction and Effect Size Estimation -- 11.1 A Simple Model -- Cross-validation -- Student-t effects -- Correlation corrections -- 11.2 Bayes and Empirical Bayes Prediction Rules -- 11.3 Prediction and Local False Discovery Rates -- 11.4 Effect Size Estimation -- False coverage rate control -- 11.5 The Missing Species Problem -- Notes -- Appendix A: Exponential Families -- A.1 Multiparameter Exponential Families -- A.2 Lindsey's Method -- Appendix B: Data Sets and Programs
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
Bibliography Includes bibliographical references and index
Notes Print version record
Subject Bayes Theorem.
Statistics as Topic.
Bayesian statistical decision theory.
Form Electronic book
ISBN 0511761368 (electronic bk.)
0511918577 (electronic bk.)
6612818743
9780511761362 (electronic bk.)
9780511918575 (electronic bk.)
9786612818745
(hardback)
(hardback)