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Efron B. — Large-Scale Inference. Empirical Bayes Methods for Estimation, Testing, and Prediction
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Название: Large-Scale Inference. Empirical Bayes Methods for Estimation, Testing, and PredictionАвтор: Efron B. Аннотация: 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 involves more than repeated application of classical methods.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 2010Количество страниц: 263Добавлена в каталог: 01.04.2012Операции: Положить на полку |
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21st century xi 1 15 240 Acceleration 139 Accuracy calculations 27 126 141 Accuracy formula 114 139 148 Alpha 146—148 250 Analysis 163—165 184 Apparent error 216 atom 217 228 229 batting averages 7 8 BAX gene 163 164 Bayes x 4 5 10 12 14 18 19 23—25 28 55 57 69 82 90 95 97 192 205 217 220 223 231 Bayes factor 45 74 Bayes intervals 233 Bayes methods 2 Bayes rule 2 3 7 13 18 53 189 211 212 230 232 233 Bayes theorem 2 27 80 188 199 217 Bayes, hierarchical 13 Bayes, objective 13 Benjamini and Hochberg x 18 23 28 46 48 52 69 Benjamini — Hochberg algorithm 48 49 54 56 57 59 64 66 69 173 204 Bin centers 116 127 129 Bin width 79 90 116 118 119 Binomial distribution 24 31 48 Bivariate normal density 117 Block statistic 150 Block test 152 Bonferroni bound 17 35 36 38 39 43 81 202 Bonferroni’s method 81 200 Boole’s inequality 35 40 Bootstrap 113 115 138—140 Bootstrap methods 112 138 Bootstrap, non-parametric 115 138 139 Brain tumor study 207 BRCA data 152 162 167 168 calculations 153 180 Canonical parameter 217 243 Cardio data 149—151 153 162 249 Central counts 98 160 161 Central matching 97 99—101 104 105 108 112 129—131 226 227 Central matching, estimates 98—100 103 104 129 130 226 Chi-square data 92 93 107 112 206 249 Chi-square distribution 4 93 Chromosome 147 148 202—205 Chromosome, sites 202 203 Clemente 7—9 Coefficient of variation 23 24 77 128 178 236 Column permutation 153 165 166 168 Combination 28 120 163 184—186 192 209 Comish — Fisher 59 135 139 Comparability 94 185 206—209 Conditional probability 2 188 197 228 Confidence interval 12 14 24 230—233 Control algorithm 48 173 204 230 231 233 Corbet, Alexander 233—237 241 Correlation x 24 26 27 51 55 56 68 77 104 106 111 114 115 117 118 128 129 141 143 146—150 152 153 155 157 159—162 165 167 174 176—178 183 220 222 223 Correlation across cases 106 108 111 113 Correlation across units 106 109 110 Correlation clusters 68 Correlation corrections 221 Correlation distribution 118 120 Correlation effects 109 139 151 159 162 176 Correlation matrix 113 117 144 149 152 222 Correlation of t-values 157 Correlation structure 42 56 174 183 221 Correlation, column 139 143—146 152 153 156 168 Correlation, count 159 Correlation, ecological 149 correlation, negative 68 111 160 162 Correlation, rms 55 56 104 106 113 122 123 141 145—149 153—157 159 176 250 Correlation, row 111 143—147 153 156 168 Correlation, row and column 141—143 Correlation, sample 67 142—144 222 Correlation, simultaneous tests of 64 67 Count vector 116 117 126 159 161 196 Covariance matrix 113 116—119 125 128 142 148 149 154 155 157 167 221 236 246 Covariate 11 80 95 107 133 147 197 198 202 206 Covariate, unobserved 107 108 111 CRAN 174 215 Cross-validation 215 216 219 221—223 240 250 Cumulant 218 230 244 Cumulant, generating function 243 244 Cumulative distribution functions (cdf) 16 18 19 32 39 41 43 51 53 54 60 68 72 91 93 105 111 113—115 119 125 132—135 138 165 169 173 237 Cumulative distribution functions (cdf), empirical 53 55 124 234 Cumulative distribution functions (cdf), non-null 86 Deconvolution 218 Delta-method 23 115 126 127 130 Demeaning 154 155 Deviance function 244 246 Dichotomous case 212 Diffusion tensor imaging 26 Dirichlet 201 245 Disease status 202 distribution 64 109 110 184 DTI data 26 28 32 34 54 57 59—61 71—73 181 182 185 186 189 199 249 Dyslexic 26 34 181 183 Dyslexic and normal children 26 193 eBay 215 218—223 240 250 EER 43 45 effect size 181 212—214 217—220 223—225 227—231 233 250 Effect size, estimation 211 212 227 230 241 Effective sample size 153 155—157 Efficiency 1 27 90 195 Eigenvalues 142—144 Eigenvector 149 151 152 Empirical Bayes ix x 1 4 5 7 10 12—14 18 20—22 27—29 37 46 51—53 55 57 63 66 69 82 88—90 114 115 190 191 198 199 212 213 217—220 223 229 231 233—235 240 241 250 Empirical Bayes, confidence intervals 12 14 233 Empirical Bayes, methods 7 17 30 37 70 113 206 209 240 Empirical Bayes, posterior band 229 Empirical distribution 20 79 109 139 169 Empirical null 84 90 91 94—98 106—108 111 112 130 141 163 167 169 183 184 186 194 224—226 250 Empirical null, density 90 164 Empirical null, distribution 56 89 160 226 227 Empirical null, estimation 97 102 194 196 Empirical probability distribution 29 Enrichment 82 163 164 167 170 171 173 174 178 181—185 191 192 194 Estimation x xi 1—3 10 13 14 20 27 28 57 58 60 71 75—77 80 82 88—90 98 99 103 104 123 156 188 195 201 220 229 233 241 243 Estimation accuracy 113 148 Estimation, effect size 211 212 227 230 241 Estimation, empirical Bayes 1 4 13 63 113 240 Estimation, empirical null 97 102 194 196 Estimation, James — Stein 10 11 209 Estimation, maximum likelihood x 1 74 75 238 245 246 Exchangeability 80 Expected false and true positives 82 83 Exponential family xi 74 82 103 104 171 174 217 224 230 243—247 Exponential family, multiparameter 105 137 245 247 Exponential family, one-parameter 137 241 243 Exponential tilting 243 244 Expression matrix 47 61 133 144 146 149 False coverage rate 230—232 False discoveries 21 22 47 51 59 232 False discovery proportion 22 23 29 47—49 51 53 55 56 106 107 130 160 201 False discovery rate x xi 18 20 22 23 26 28 30 37 42 43 45—17 50 53 57 58 60 62 64 69 70 72 73 81—83 97 102 105 106 128 159 160 164 184—186 188 194 197—201 205 208 212 223 225 False discovery rate, Bayes 18 19 23—25 29 55 200 False discovery rate, local 19 28 29 57 70 73 77 78 82 83 86—88 90 97 183 185 187 197 223 226 229 250 False discovery rate, positive 51 False negative rate 57 69 FCR control 230 231 233 FDR control 30 37 45 46 48 50 51 57 58 69 70 173 204 231 233 Filtration 109 Fisher, R.A. ix x 14 15 31 32 36 45 48 65 111 112 234 237—239 241 Fisher’s linear discriminant function 211 212 214 Fisher’s prediction formula 237 Fisher’s scale of evidence 31 46 Fold-change 207—209 Frequentist ix x 1 2 5 10 14 15 18 30 37 48 54 115 199 200 205 230 233 Frequentist, methods 205 233 FWER 30 34 35 43 44 47 49 50 81 83 185 199 200 205 FWER, control 35 37 40 43 Gamma density 237 Gamma distribution 134 Gene expression 15 141 149 163 167 212 Gene set 163—171 173 174 176 181 183 184 Generalized linear model (GLM) 75 127 247 Generalized linear model (GLM), Poisson 131 247 248 GSEA statistic 165 172—174 Hermite polynomial 118 119 Hierarchical model 241 Hierarchical model, Bayes 27 28 96 182 Hierarchical model, normal 217 223—226 228 241 Hierarchical model, Poisson 240 High-dimensional statistical inference 1 Higher criticism 59 69 205 Hippocampus 197 HIV data 94 96 99 105 110—112 148 249 Holm’s procedure 36—38 40 81 Homogeneity assumption 123—125 Hyperparameter 13 Independence 24—26 36 39 50 55 56 59 66 76 84 92 106 111 113 124 125 128 130 141 152 153 221 222 235 236 Independence, assumption 24 26 55 60 106 Independence, column-wise 141 149 153 162 Indirect evidence 7 229 240 Influence function 127 129 130 139 James — Stein estimator 1 5—7 14 27 Jensen’s Inequality 22 23 155 K-FWER 43—45 Kidney data 11 14 249 Kolmogorov — Smimov test statistic 165 172 Kronecker product 154 Kullback — Leibler distance 244 kurtosis 132 135 Large-scale inference 3 9 34 163 Learning from the experience of others 10 27 184 206 229 240 Least squares 10 12 110 129 131 245 Lehmann alternatives 20 Leukemia data 63 64 98 111—114 124 132 138 146 147 224 225 249 Likelihood, x 1—3 5 13 74 75 102—104 171 238 245 246 Limma 184 Lindsey’s method 74—76 88 247 Linear logistic model 194 195 Linear regression 5 11 34 150 152 240 Local averaging 181—183 Local true discovery rate 84 Locfdr 34 75 76 82 86 101 103 104 127 153 226 250 Logistic regression estimate 189 Malaysian butterfly data 233 234 236 Marginal density 18 19 123 187 188 199 217 218 224 233 Marginal distribution 2 4 177 Max-T 40—43 Maximum likelihood estimator (MLE) 3 5 102 Maxmean statistic 171—173 184 Mean 2 8 9 24 28 56 68 77 87 98 104 107 115—117 121 125 126 132—135 137 141—144 147 149 154 156—159 161 165—168 172 173 177 178 184 211 214 250 Mean and variance 6 23 60 82 114 144 158 159 161 180 228 230 244 Mean, posterior 13 218 223 Mehler’s identity 118 121 Michigan lung cancer study 222 223 241 Microarray ix 1 15 27 28 43 45 61 81 91 96 106 107 109 121 141 143 145 148—150 152 163 164 167 181 206—208 212 215 Microarray experiment 61 107 112 133 143 152 163 223 Microarray study 27 61 64 91 109 113 148 163 Miller, Rupert xi 30 45 186 205 MIN 40 41 Missing mass problem 239 Missing species problem 233 237 241 Mixture density 18 21 29 71 74 88 96 101 114 187 250 MLE method 1 90 99 101 102 104 105 108 112 153 183 189 Multi-class model 117 119 187 multinomial 118 125 161 236 245 247 Multivariate normal 2 6 28 36 146 211 245 Natural parameter 137 217 243 244 247 Natural spline basis 76 90 Nearest shrunken centroid 215 240 Negative binomial 237 238 New species 234 235 237 238 Non-central 1 178 180 Non-central t 132 137 221 Non-central t, distribution 133 Non-null counts 84 85 Non-null counts, smoothed 84 85 96 124 Normal distribution 3 16 84 139 153 213 Normal distribution, matrix normal 154 Normal distribution, multivariate normal 211 Null and alternative densities 29 Null hypothesis x 16 26 31 32 48 49 51 55 58 65 74 83 89 96 97 105 111 113 132 135—137 141 149—151 164 165 170—172 174 194 195 201 224 227 250 Null hypothesis, blurry 97 Null hypothesis, complete 40—42 Null hypothesis, enrichment 194 Null proportion 20 28 49 54 60 66 90 98 Odds ratio 2 211 227 Optimal discovery procedure 45 p-values 31—41 45 48—53 57 66 70 136 141 167 169 173 174 200 204 P-values, adjusted 34—37 39—42 202 P53 data 163 166 173 184 194 250 P53 data, P53_UP 194 195 Pamr 215—219 240 PCER 43 Penalty 5 50 76 201 204 205 Penalty, correlation 114 118 119 122 123 128 Permutation algorithms 39 Permutation calculations 40 97 109 110 177—180 183 Permutation distribution 41 62 64 89 111 169 180 Permutation methods 41 42 110—112 149 171 174 Permutation null 97 109 111 141 149 Point estimate 22 Poisson assumption 25 170 Poisson deviance 76 248 Poisson process 234 Poisson regression 71 75 218 219 245 Poisson regression, estimate 74 114 123 127 196 233 Poisson selection model 170 174 Poisson-independence 24 25 58 200 Police data 93 95 112 226 227 249 Positive regression dependence 50 69 Posterior distribution 2 3 12 229 Posterior interval 12 13 232 Posterior probability 18 53 57 74 95 Power 34 48 57 74 83 85—89 104 153 163 170—173 Power, diagnostics 83 87 88 Prediction xi 1 7—10 28 211—217 223 228 229 234 235 237—241 Prediction error 7 214 219—221 Prediction rule 97 211—213 216 217 219—221 223 Prediction rule, ideal 213 Prediction, computer-intensive 212 Prior density 2 27 95—97 228 Prior knowledge 80 88 Prior probability 17 70 83 187 211 213 Prostate data 15 17 21 24 27 41 42 44 47 50 57 60—63 68 71—73 78—80 82 84 85 88 148 151 184 185 207 208 212 214—216 219 221 224 225 229 249 250 R-test x 28 32 64—66 68 69 91 96 112 149 163 168 249 Randomization 164—167 169 174 176 179 Ras pathway 164 166 171 Relevance x 81 82 94 185 186 196—198 205 206 209 Relevance function 14 197 198 209 Restandardization 168 169 173 174 176 178 179 183 184 Restandardization, restandardized 168 173 184 Risk function 3 Rms approximation 121—123 125 161 Robbins, Herbert x 1 14 88 240 241 Row 165 167—171 174 177 183 184 SAM 61—64 94 110 174 209 Scaling properties 80 81 Score function 171 246 Scoring function 165 169 170 174 Secant 19 Second derivative matrix 246 Selection bias 215 230 Separate analyses 185 186 199 205 Separation 184—186 196 199 200 205 209 Shakespeare data 238 239 241 250 Shakespeare, Wm. 238—241 Shakespeare, Wm., canon 238 239 Sidak procedure 36 37
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