Large-scale inference: empirical Bayes methods for estimation, testing, and prediction
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2013
|
| Edition: | 1. paperback ed. |
| Series: | Institute of Mathematical Statistics monographs
1 |
| Subjects: | |
| Online Access: | http://digitool.hbz-nrw.de:1801/webclient/DeliveryManager?pid=3924165&custom%5Fatt%5F2=simple%5Fviewer Inhaltsverzeichnis |
| Physical Description: | XII, 263 S. graph. Darst. |
| ISBN: | 9780521192491 0521192498 9781107619678 |
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Record in the Search Index
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| adam_text | Titel: Large scale inference
Autor: Efron, Bradley
Jahr: 2010
Contents
Prologue ix
Acknowledgments xii
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
Contents
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
Contents vii
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
Appendix A Exponential Families 243
A. 1 Multiparameter Exponential Families 245
A.2 Lindsey s Method 247
Appendix B Data Sets and Programs 249
References 251
Index 258
|
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| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 1. paperback ed. |
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| indexdate | 2024-07-09T22:55:11Z |
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| isbn | 9780521192491 0521192498 9781107619678 |
| language | English |
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| spelling | Efron, Bradley 1938- Verfasser (DE-588)142290718 aut Large-scale inference empirical Bayes methods for estimation, testing, and prediction Bradley Efron large scale 1. paperback ed. Cambridge [u.a.] Cambridge Univ. Press 2013 XII, 263 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Institute of Mathematical Statistics monographs 1 Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd rswk-swf Schätztheorie (DE-588)4121608-8 gnd rswk-swf Statistischer Test (DE-588)4077852-6 gnd rswk-swf Statistische Schlussweise (DE-588)4182963-3 gnd rswk-swf Statistische Schlussweise (DE-588)4182963-3 s Schätztheorie (DE-588)4121608-8 s Statistischer Test (DE-588)4077852-6 s Bayes-Entscheidungstheorie (DE-588)4144220-9 s DE-604 Institute of Mathematical Statistics monographs 1 (DE-604)BV037337077 1 http://digitool.hbz-nrw.de:1801/webclient/DeliveryManager?pid=3924165&custom%5Fatt%5F2=simple%5Fviewer HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021194372&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Efron, Bradley 1938- Large-scale inference empirical Bayes methods for estimation, testing, and prediction Institute of Mathematical Statistics monographs Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd Schätztheorie (DE-588)4121608-8 gnd Statistischer Test (DE-588)4077852-6 gnd Statistische Schlussweise (DE-588)4182963-3 gnd |
| subject_GND | (DE-588)4144220-9 (DE-588)4121608-8 (DE-588)4077852-6 (DE-588)4182963-3 |
| title | Large-scale inference empirical Bayes methods for estimation, testing, and prediction |
| title_alt | large scale |
| title_auth | Large-scale inference empirical Bayes methods for estimation, testing, and prediction |
| title_exact_search | Large-scale inference empirical Bayes methods for estimation, testing, and prediction |
| title_full | Large-scale inference empirical Bayes methods for estimation, testing, and prediction Bradley Efron |
| title_fullStr | Large-scale inference empirical Bayes methods for estimation, testing, and prediction Bradley Efron |
| title_full_unstemmed | Large-scale inference empirical Bayes methods for estimation, testing, and prediction Bradley Efron |
| title_short | Large-scale inference |
| title_sort | large scale inference empirical bayes methods for estimation testing and prediction |
| title_sub | empirical Bayes methods for estimation, testing, and prediction |
| topic | Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd Schätztheorie (DE-588)4121608-8 gnd Statistischer Test (DE-588)4077852-6 gnd Statistische Schlussweise (DE-588)4182963-3 gnd |
| topic_facet | Bayes-Entscheidungstheorie Schätztheorie Statistischer Test Statistische Schlussweise |
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