Large-scale inference : empirical Bayes methods for estimation, testing, and prediction /
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| Author / Creator: | Efron, Bradley. |
|---|---|
| Imprint: | Cambridge : Cambridge University Press, 2010. |
| Description: | xii, 263 p. : ill. (some col.) ; 24 cm. |
| Language: | English |
| Series: | Institute of mathematical statistics monographs ; 1 Institute of Mathematical Statistics monographs ; 1. |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/8151123 |
Table of 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
- 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
- 8.2. Estimating the Root Mean Square Correlation
- 8.3. Are a Set of Microarrays Independent of Each Other?
- 8.4. Multivariate Normal Calculations
- 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
- 10.3. Relevance
- 10.4. Are Separate Analyses Legitimate?
- 10.5. Comparability
- Notes
- 11. Prediction and Effect Size Estimation
- 11.1. A Simple Model
- 11.2. Bayes and Empirical Bayes Prediction Rules
- 11.3. Prediction and Local False Discovery Rates
- 11.4. Effect Size Estimation
- 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
- References
- Index
