Computer age statistical inference: algorithms, evidence, and data science
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge, United Kingdom ; New York, NY, USA
Cambridge University Press
2016
|
| Schriftenreihe: | Institute of Mathematical Statistics monographs
5 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | xix, 475 Seiten Illustrationen, Diagramme |
| ISBN: | 9781107149892 |
Internformat
MARC
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
Preface xv
Acknowledgments xviii
Notation xix
Part I Classic Statistical Inference l
1 Algorithms and Inference 3
LI A Regression Example 4
1.2 Hypothesis Testing 8
1.3 Notes 11
2 F requentist Inference 12
2.1 Frequentism in Practice 14
2.2 Frequentist Optimality 18
2.3 Notes and Details 20
3 Bayesian Inference 22
3.1 Two Examples 24
3.2 Uninformative Prior Distributions 28
3.3 Flaws in Frequentist Inference 30
3.4 A Bayesian/Frequentist Comparison List 33
3.5 Notes and Details 36
4 Fisherian Inference and Maximum Likelihood Estimation 38
4.1 Likelihood and Maximum Likelihood 38
4.2 Fisher Information and the MLE 41
4.3 Conditional Inference 45
4.4 Permutation and Randomization 49
4.5 Notes and Details 51
5 Parametric Models and Exponential Families 53
IX
X
Contents
5.1 Univariate Families 54
5.2 The Multivariate Normal Distribution 55
5.3 Fisher’s Information Bound for Multiparameter Families 59
5.4 The Multinomial Distribution 61
5.5 Exponential Families 64
5.6 Notes and Details 69
Part II Early Computer-Age Methods 73
6 Empirical Bayes 75
6.1 Robbins’ Formula 75
6.2 The Missing-Species Problem 78
6.3 A Medical Example 84
6.4 Indirect Evidence 1 88
6.5 Notes and Details 88
7 James-Stein Estimation and Ridge Regression 91
7.1 The James-Stein Estimator 91
7.2 The Baseball Players 94
7.3 Ridge Regression 97
7.4 Indirect Evidence 2 102
7.5 Notes and Details 104
8 Generalized Linear Models and Regression Trees 108
8.1 Logistic Regression 109
8.2 Generalized Linear Models 116
8.3 Poisson Regression 120
8.4 Regression Trees 124
8.5 Notes and Details 128
9 Survival Analysis and the EM Algorithm 131
9.1 Life Tables and Hazard Rates 131
9.2 Censored Data and the Kaplan-Meier Estimate 134
9.3 The Log-Rank Test 139
9.4 The Proportional Hazards Model 143
9.5 Missing Data and the EM Algorithm 146
9.6 Notes and Details 150
10 The Jackknife and the Bootstrap 155
10.1 The Jackknife Estimate of Standard Error 156
10.2 The Nonparametric Bootstrap 159
10.3 Resampling Plans 162
Contents
xi
10.4 The Parametric Bootstrap 169
10.5 Influence Functions and Robust Estimation 174
10.6 Notes and Details 177
11 Bootstrap Confidence Intervals 181
11.1 Neyman’s Construction for One-Parameter Problems 181
11.2 The Percentile Method 185
11.3 Bias-Corrected Confidence Intervals 190
11.4 Second-Order Accuracy 192
11.5 Bootstrap-? Intervals 195
11.6 Objective Bayes Intervals and the Confidence Distribution 198
11.7 Notes and Details 204
12 Cross-Validation and Cp Estimates of Prediction Error 208
12.1 Prediction Rules 208
12.2 Cross-Validation 213
12.3 Covariance Penalties 218
12.4 Training, Validation, and Ephemeral Predictors 227
12.5 Notes and Details 230
13 Objective Bayes Inference and MCMC 233
13.1 Objective Prior Distributions 234
13.2 Conjugate Prior Distributions 237
13.3 Model Selection and the Bayesian Information Criterion 243
13.4 Gibbs Sampling and MCMC 251
13.5 Example: Modeling Population Admixture 256
13.6 Notes and Details 261
14 Postwar Statistical Inference and Methodology 264
Part III Twenty-First-Century Topics 269
15 Large-Scale Hypothesis Testing and FDRs 271
15.1 Large-Scale Testing 272
15.2 False-Discovery Rates 275
15.3 Empirical Bayes Large-Scale Testing 278
15.4 Local False-Discovery Rates 282
15.5 Choice of the Null Distribution 286
15.6 Relevance 290
15.7 Notes and Details 294
16 Sparse Modeling and the Lasso 298
xii Contents
16.1 Forward Stepwise Regression 299
16.2 The Lasso 303
16.3 Fitting Lasso Models 308
16.4 Least-Angle Regression 309
16.5 Fitting Generalized Lasso Models 313
16.6 Post-Selection Inference for the Lasso 317
16.7 Connections and Extensions 319
16.8 Notes and Details 321
17 Random Forests and Boosting 324
17.1 Random Forests 325
17.2 Boosting with Squared-Error Loss 333
17.3 Gradient Boosting 338
17.4 Adaboost: the Original Boosting Algorithm 341
17.5 Connections and Extensions 345
17.6 Notes and Details 347
18 Neural Networks and Deep Learning 351
18.1 Neural Networks and the Handwritten Digit Problem 353
18.2 Fitting a Neural Network 356
18.3 Autoencoders 362
18.4 Deep Learning 364
18.5 Learning a Deep Network 368
18.6 Notes and Details 371
19 Support-Vector Machines and Kernel Methods 375
19.1 Optimal Separating Hyperplane 376
19.2 Soft-Margin Classifier 378
19.3 SVM Criterion as Loss Plus Penalty 379
19.4 Computations and the Kernel Trick 381
19.5 Function Fitting Using Kernels 384
19.6 Example: String Kernels for Protein Classification 385
19.7 SVMs: Concluding Remarks 387
19.8 Kernel Smoothing and Local Regression 387
19.9 Notes and Details 390
20 Inference After Model Selection 394
20.1 Simultaneous Confidence Intervals 395
20.2 Accuracy After Model Selection 402
20.3 Selection Bias 408
20.4 Combined Bayes-Frequentist Estimation 412
20.5 Notes and Details 417
Contents xiii
21 Empirical Bayes Estimation Strategies 421
21.1 Bayes Deconvolution 421
21.2 g-Modeling and Estimation 424
21.3 Likelihood, Regularization, and Accuracy 427
21.4 Two Examples 432
21.5 Generalized Linear Mixed Models 437
21.6 Deconvolution and /-Modeling 440
21.7 Notes and Details 444
Epilogue 446
References 453
Author Index 463
Subject Index 467
|
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| spelling | Efron, Bradley 1938- Verfasser (DE-588)142290718 aut Computer age statistical inference algorithms, evidence, and data science Bradley Efron (Stanford University, California), Trevor Hastie (Stanford University, California) Cambridge, United Kingdom ; New York, NY, USA Cambridge University Press 2016 xix, 475 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Institute of Mathematical Statistics monographs 5 Hier auch später erschienene, unveränderte Nachdrucke Geschichte gnd rswk-swf Big Data (DE-588)4802620-7 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Geschichte (DE-588)4020517-4 gnd rswk-swf Statistische Schlussweise (DE-588)4182963-3 gnd rswk-swf Statistik (DE-588)4056995-0 s Statistische Schlussweise (DE-588)4182963-3 s Big Data (DE-588)4802620-7 s Geschichte z DE-604 Geschichte (DE-588)4020517-4 s 1\p DE-604 Hastie, Trevor 1953- Verfasser (DE-588)172128242 aut Institute of Mathematical Statistics monographs 5 (DE-604)BV037337077 5 Digitalisierung UB Bamberg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028982659&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Efron, Bradley 1938- Hastie, Trevor 1953- Computer age statistical inference algorithms, evidence, and data science Institute of Mathematical Statistics monographs Big Data (DE-588)4802620-7 gnd Statistik (DE-588)4056995-0 gnd Geschichte (DE-588)4020517-4 gnd Statistische Schlussweise (DE-588)4182963-3 gnd |
| subject_GND | (DE-588)4802620-7 (DE-588)4056995-0 (DE-588)4020517-4 (DE-588)4182963-3 |
| title | Computer age statistical inference algorithms, evidence, and data science |
| title_auth | Computer age statistical inference algorithms, evidence, and data science |
| title_exact_search | Computer age statistical inference algorithms, evidence, and data science |
| title_full | Computer age statistical inference algorithms, evidence, and data science Bradley Efron (Stanford University, California), Trevor Hastie (Stanford University, California) |
| title_fullStr | Computer age statistical inference algorithms, evidence, and data science Bradley Efron (Stanford University, California), Trevor Hastie (Stanford University, California) |
| title_full_unstemmed | Computer age statistical inference algorithms, evidence, and data science Bradley Efron (Stanford University, California), Trevor Hastie (Stanford University, California) |
| title_short | Computer age statistical inference |
| title_sort | computer age statistical inference algorithms evidence and data science |
| title_sub | algorithms, evidence, and data science |
| topic | Big Data (DE-588)4802620-7 gnd Statistik (DE-588)4056995-0 gnd Geschichte (DE-588)4020517-4 gnd Statistische Schlussweise (DE-588)4182963-3 gnd |
| topic_facet | Big Data Statistik Geschichte Statistische Schlussweise |
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| volume_link | (DE-604)BV037337077 |
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