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Efron B. Ч Large-Scale Interference. Empirical Bayes Methods for Estimation, Testing, and Prediction
Efron B. Ч Large-Scale Interference. Empirical Bayes Methods for Estimation, Testing, and Prediction

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Ќазвание: Large-Scale Interference. Empirical Bayes Methods for Estimation, Testing, and Prediction

јвтор: Efron B.

јннотаци€:

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.


язык: en

–убрика: ћатематика/

—ери€: —делано в холле

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

»здание: 1

√од издани€: 2010

 оличество страниц: 275

ƒобавлена в каталог: 01.04.2012

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
21st century      xi 1 15 240
Acceleration      139
Accuracy calculations      27 126 141
Accuracy formula      114 139 148
Alpha      146Ч148 250
Apparent error      216
atom      217 228 229
batting averages      7 8
BAX gene      163 164
Bayes      x 4 5 10 12 14 18 19 23Ч25 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 Ч 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 138Ч140
Bootstrap methods      112 138
Bootstrap, non-parametric      115 138 139
Brain tumor study      207
BRCA data      152 162 167 168
Canonical parameter      217 243
Cardio data      149Ч151 153 162 249
Central counts      98 160 161
Central matching      97 99Ч101 104 105 108 112 129Ч131 226 227
Central matching, estimates      98Ч100 103 104 129 130 226
Chi-square data      92 93 107 112 206 249
Chi-square distribution      4 93
Chromosome      147 148 202Ч205
Chromosome, sites      202 203
Clemente      7Ч9
Coefficient of variation      23 24 77 128 178 236
Column permutation      153 165 166 168
Combination      28 120 163 184Ч186 192 209
Comparability      94 185 206Ч209
Conditional probability      2 188 197 228
Confidence interval      12 14 24 230Ч233
Control algorithm      48 173 204 230 231 233
Corbet, Alexander      233Ч237 241
Cornish Ч Fisher      59 135 139
Correlation      x 24 26 27 51 55 56 68 77 104 106 111 114 115 117 118 128 129 141 143 146Ч150 152 153 155 157 159Ч162 165 167 174 176Ч178 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 143Ч146 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 145Ч149 153Ч157 159 176 250
Correlation, row      111 143Ч147 153 156 168
Correlation, row and column      141Ч143
Correlation, sample      67 142Ч144 222
Correlation, simultaneous tests of      64 67
Count vector      116 117 126 159 161 196
Covariance matrix      113 116Ч119 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 221Ч223 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 113Ч115 119 125 132Ч135 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
DTI data      26 28 32 34 54 57 59Ч61 71Ч73 181 182 185 186 189 199 249
Dyslexic      26 34 181 183
Dyslexic and normal children      26 193
eBay      215 218Ч223 240 250
EER      43 45
effect size      181 212Ч214 217Ч220 223Ч225 227Ч231 233 250
Effect size, estimation      211 212 227 230 241
Effective sample size      153 155Ч157
Efficiency      1 27 90 195
Eigenvalues      142Ч144
Eigenvector      149 151 152
Empirical Bayes      ix x 1 4 5 7 10 12Ч14 18 20Ч22 27Ч29 37 46 51Ч53 55 57 63 66 69 82 88Ч90 114 115 190 191 198 199 212 213 217Ч220 223 229 231 233Ч235 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 94Ч98 106Ч108 111 112 130 141 163 167 169 183 184 186 194 224Ч226 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 181Ч185 191 192 194
Enrichment, analysis      163Ч165 184
Estimation      x xi 1Ч3 10 13 14 20 27 28 57 58 60 71 75Ч77 80 82 88Ч90 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 Ч 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 243Ч247
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      230Ч232
False discoveries      21 22 47 51 59 232
False discovery proportion      22 23 29 47Ч49 51 53 55 56 106 107 130 160 201
False discovery rate      x xi 18 20 22 23 26 28 30 37 42 43 45Ч17 50 53 57 58 60 62 64 69 70 72 73 81Ч83 97 102 105 106 128 159 160 164 184Ч186 188 194 197Ч201 205 208 212 223 225
False discovery rate, Bayes      18 19 23Ч25 29 55 200
False discovery rate, local      19 28 29 57 70 73 77 78 82 83 86Ч88 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 237Ч239 241
Fisher, R.A., Fisher's linear discriminant function      211 212 214
Fisher, R.A., Fisher's prediction formula      237
Fisher, R.A., Fisher's scale of evidence      31 46
Fold-change      207Ч209
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      163Ч171 173 174 176 181 183 184
Generalized linear model (GLM)      75 127 247
Generalized linear model (GLM), Poisson      131 247 248
GSEA statistic      165 172Ч174
Hermite polynomial      118 119
Hierarchical model      241
Hierarchical model, Bayes      27 28 96 182
Hierarchical model, normal      217 223Ч226 228 241
Hierarchical model, Poisson      240
High-dimensional statistical inference      1
Higher criticism      59 69 205
Hippocampus      197
HIV data      94 96 99 105 110Ч112 148 249
Holm's procedure      36Ч38 40 81
Homogeneity assumption      123Ч125
Hyperparameter      13
Independence      24Ч26 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 Ч Stein estimator      1 5Ч7 14 27
Jensen's inequality      22 23 155
K-FWER      43Ч4Ч5
Kidney data      11 14 249
Kolmogorov Ч Smirnov test statistic      165 172
Kronecker product      154
Kullback Ч 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 111Ч114 124 132 138 146 147 224 225 249
Likelihood      x 1Ч3 5 13 74 75 102Ч104 171 238 245 246
Limma      184
Lindsey's method      74Ч76 88 247
Linear logistic model      194 195
Linear regression      5 11 34 150 152 240
Local averaging      181Ч183
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      40Ч43
Maximum likelihood estimator (MLE)      3 5 102
Maxmean statistic      171Ч173 184
Mean      2 8 9 24 28 56 68 77 87 98 104 107 115Ч117 121 125 126 132Ч135 137 141Ч144 147 149 154 156Ч159 161 165Ч168 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 148Ч150 152 163 164 167 181 206Ч208 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-p      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
Multivariate normal, calculations      153 180
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 $\chi^{2}$      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 135Ч137 141 149Ч151 164 165 170Ч172 174 194 195 201 224 227 250
Null hypothesis, blurry      97
Null hypothesis, complete      40Ч42
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      31Ч41 45 48Ч53 57 66 70 136 141 167 169 173 174 200 204
P-values, adjusted      34Ч37 39Ч42 202
P53 data      163 166 173 184 194 250
P53 data, P53_UP      194 195
Pamr      215Ч219 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 177Ч180 183
Permutation distribution      41 62 64 89 111 169 180
Permutation methods      41 42 110Ч112 149 171 174
Permutation null      97 109 111 141 149
Permutation null, distribution      64 109 110 184
Point estimate      22
Poisson assumption      25 170
Poisson assumption, Poisson-independence      24 25 58 200
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
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 85Ч89 104 153 163 170Ч173
Power, diagnostics      83 87 88
Prediction      xi 1 7Ч10 28 211Ч217 223 228 229 234 235 237Ч241
Prediction error      7 214 219Ч221
Prediction rule      97 211Ч213 216 217 219Ч221 223
Prediction rule, ideal      213
Prediction, computer-intensive      212
Prior density      2 27 95Ч97 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 60Ч63 68 71Ч73 78Ч80 82 84 85 88 148 151 184 185 207 208 212 214Ч216 219 221 224 225 229 249 250
Randomization      164Ч167 169 174 176 179
Randomization, row      165 167Ч171 174 177 183 184
Ras pathway      164 166 171
Relevance      x 81 82 94 185 186 196Ч198 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      121Ч123 125 161
Robbins, Herbert      x 1 14 88 240 241
SAM      61Ч64 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      184Ч186 196 199 200 205 209
Shakespeare data      238 239 241 250
Shakespeare, Wm.      238Ч241
Shakespeare, Wm., canon      238 239
Sidak procedure      36 37
Significance level      34 81 178 200
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