2010, Institute of mathematical statistics monographs, ISBN 0521192498, Volume 1, xii, 263

.... 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...

Bayesian statistical decision theory | Economics | Study and teaching

Bayesian statistical decision theory | Economics | Study and teaching

Book

The Annals of statistics, ISSN 0090-5364, 08/2007, Volume 35, Issue 4, pp. 1351 - 1377

Modern scientific technology has provided a new class of large-scale simultaneous inference problems, with thousands of hypothesis tests to consider at the...

Maximum likelihood estimation | Histograms | Density estimation | Estimate reliability | Scientific method | Null hypothesis | Standard deviation | Multiple Testing and High-Dimensional Data | Prostate | Statistics | Estimation methods | Empirical Bayes | Local false discovery rates | Large-scale simultaneous inference | Empirical null | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | empirical null | large-scale simultaneous inference | 62G07 | empirical Bayes | 62J07

Maximum likelihood estimation | Histograms | Density estimation | Estimate reliability | Scientific method | Null hypothesis | Standard deviation | Multiple Testing and High-Dimensional Data | Prostate | Statistics | Estimation methods | Empirical Bayes | Local false discovery rates | Large-scale simultaneous inference | Empirical null | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | empirical null | large-scale simultaneous inference | 62G07 | empirical Bayes | 62J07

Journal Article

Journal of the American Statistical Association, ISSN 0162-1459, 03/2004, Volume 99, Issue 465, pp. 96 - 104

Current scientific techniques in genomics and image processing routinely produce hypothesis testing problems with hundreds or thousands of cases to consider...

Unobserved covariates | Empirical null hypothesis | Local false discovery rate | Empirical bayes | Microarray analysis | Hypothesis testing | Histograms | Null hypothesis | Scientific method | Approximation | Theory and Methods | Memory interference | Correlations | Inference | Genetic mutation | Estimation methods | Empirical Bayes | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Statistics | Methods

Unobserved covariates | Empirical null hypothesis | Local false discovery rate | Empirical bayes | Microarray analysis | Hypothesis testing | Histograms | Null hypothesis | Scientific method | Approximation | Theory and Methods | Memory interference | Correlations | Inference | Genetic mutation | Estimation methods | Empirical Bayes | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Statistics | Methods

Journal Article

07/2016, Institute of Mathematical Statistics Monographs, ISBN 1107149894, Volume 5, 433

The twenty-first century has seen a breathtaking expansion of statistical methodology, both in scope and in influence. 'Big data', 'data science', and 'machine...

Mathematical statistics

Mathematical statistics

eBook

Journal of the American Statistical Association, ISSN 1537-274X, 07/2013, Volume 109, Issue 507, pp. 991 - 1007

Classical statistical theory ignores model selection in assessing estimation accuracy. Here we consider bootstrap methods for computing standard errors and...

Bootstrap smoothing | p | C | ABC intervals | Lasso | Model averaging | Bagging | Importance sampling | Estimation bias | Supernovae | Theory and Methods | Standard deviation | Standard error | Nonparametric models | Cholesterols | Estimators | Confidence interval | Bootstrap resampling | Estimation methods | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Regression analysis | Bootstrapping (Statistics) | Analysis | Nonparametric statistics | model averaging | bagging | importance sampling | bootstrap smoothing | Cp

Bootstrap smoothing | p | C | ABC intervals | Lasso | Model averaging | Bagging | Importance sampling | Estimation bias | Supernovae | Theory and Methods | Standard deviation | Standard error | Nonparametric models | Cholesterols | Estimators | Confidence interval | Bootstrap resampling | Estimation methods | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Regression analysis | Bootstrapping (Statistics) | Analysis | Nonparametric statistics | model averaging | bagging | importance sampling | bootstrap smoothing | Cp

Journal Article

The annals of applied statistics, ISSN 1932-6157, 12/2012, Volume 6, Issue 4, pp. 1971 - 1997

The parametric bootstrap can be used for the efficient computation of Bayes posterior distributions. Importance sampling formulas take on an easy form relating...

Maximum likelihood estimation | Histograms | Estimate reliability | Bayes estimators | Inference | Mathematical vectors | Bayesian inference | Skewed distribution | Frequentism | Estimation methods | Exponential families | Jeffreys prior | Deviance | Generalized linear models | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Statistics - Applications | generalized linear models | exponential families | deviance

Maximum likelihood estimation | Histograms | Estimate reliability | Bayes estimators | Inference | Mathematical vectors | Bayesian inference | Skewed distribution | Frequentism | Estimation methods | Exponential families | Jeffreys prior | Deviance | Generalized linear models | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Statistics - Applications | generalized linear models | exponential families | deviance

Journal Article

The annals of applied statistics, ISSN 1932-6157, 06/2007, Volume 1, Issue 1, pp. 107 - 129

This paper discusses the problem of identifying differentially expressed groups of genes from a microarray experiment. The groups of genes are externally...

Datasets | Histograms | Null hypothesis | Databases | Genes | Random allocation | P values | Standard deviation | Descriptive statistics | Statistics | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology

Datasets | Histograms | Null hypothesis | Databases | Genes | Random allocation | P values | Standard deviation | Descriptive statistics | Statistics | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology

Journal Article

Journal of biopharmaceutical statistics, ISSN 1520-5711, 10/2011, Volume 21, Issue 6, pp. 1052 - 1062

This note concerns the use of parametric bootstrap sampling to carry out Bayesian inference calculations. This is only possible in a subset of those problems...

MCMC | Gibbs sampling | Bayes credible intervals | Importance sampling | Statistics & Probability | Pharmacology & Pharmacy | Physical Sciences | Mathematics | Life Sciences & Biomedicine | Science & Technology | Monte Carlo Method | Markov Chains | Bayes Theorem | Monte Carlo methods | Computation | Mathematical analysis | Inference | Sampling | Bayesian analysis | Statistics | Index Medicus | importance sampling

MCMC | Gibbs sampling | Bayes credible intervals | Importance sampling | Statistics & Probability | Pharmacology & Pharmacy | Physical Sciences | Mathematics | Life Sciences & Biomedicine | Science & Technology | Monte Carlo Method | Markov Chains | Bayes Theorem | Monte Carlo methods | Computation | Mathematical analysis | Inference | Sampling | Bayesian analysis | Statistics | Index Medicus | importance sampling

Journal Article

The annals of applied statistics, ISSN 1932-6157, 03/2008, Volume 2, Issue 1, pp. 197 - 223

Modern statisticians are often presented with hundreds or thousands of hypothesis testing problems to evaluate at the same time, generated from new scientific...

Enrichment | False discovery rates | Separate-class model | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Statistics - Applications | enrichment | separate-class model

Enrichment | False discovery rates | Separate-class model | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Statistics - Applications | enrichment | separate-class model

Journal Article

The annals of applied statistics, ISSN 1932-6157, 9/2009, Volume 3, Issue 3, pp. 922 - 942

Having observed an m x n matrix X whose rows are possibly correlated, we wish to test the hypothesis that the columns are independent of each other. Our...

Histograms | Statistical variance | Null hypothesis | Estimate reliability | Permutation tests | Correlations | Standardization | Eigenvalues | Matrices | Covariance matrices | Effective sample size | Matrix normal distribution | Total correlation | Row and column correlations | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Statistics - Applications | row and column correlations | matrix normal distribution | effective sample size | permutation tests | total correlation

Histograms | Statistical variance | Null hypothesis | Estimate reliability | Permutation tests | Correlations | Standardization | Eigenvalues | Matrices | Covariance matrices | Effective sample size | Matrix normal distribution | Total correlation | Row and column correlations | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Statistics - Applications | row and column correlations | matrix normal distribution | effective sample size | permutation tests | total correlation

Journal Article

Journal of the American Statistical Association, ISSN 1537-274X, 03/2007, Volume 102, Issue 477, pp. 93 - 103

Large-scale hypothesis testing problems, with hundreds or thousands of test statistics z
i
to consider at once, have become familiar in current practice....

False discovery rate | Correlated processes | Microarray | Empirical null | Histograms | Statistical variance | Null hypothesis | Approximation | Theory and Methods | Correlations | Null condition | Inference | Breast cancer | Standard deviation | Covariance matrices | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Usage | Correlation (Statistics) | Analysis | Hypothesis

False discovery rate | Correlated processes | Microarray | Empirical null | Histograms | Statistical variance | Null hypothesis | Approximation | Theory and Methods | Correlations | Null condition | Inference | Breast cancer | Standard deviation | Covariance matrices | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Usage | Correlation (Statistics) | Analysis | Hypothesis

Journal Article

Statistical science, ISSN 0883-4237, 02/2008, Volume 23, Issue 1, pp. 1 - 22

The classic frequentist theory of hypothesis testing developed by Neyman, Pearson and Fisher has a claim to being the twentieth century's most influential...

Hypothesis testing | Histograms | Null hypothesis | Correlations | Standard deviation | Frequentism | Statistics | Modeling | Prostate | Mathematical permutation | False discovery rates | Simultaneous tests | Empirical null | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Statistics - Methodology | empirical null | false discovery rates

Hypothesis testing | Histograms | Null hypothesis | Correlations | Standard deviation | Frequentism | Statistics | Modeling | Prostate | Mathematical permutation | False discovery rates | Simultaneous tests | Empirical null | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Statistics - Methodology | empirical null | false discovery rates

Journal Article

Journal of the American Statistical Association, ISSN 0162-1459, 04/2020, Volume 115, Issue 530, pp. 636 - 655

The scientific needs and computational limitations of the twentieth century fashioned classical statistical methodology. Both the needs and limitations have...

Black box | Surface plus noise | Ephemeral predictors | Random forests | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Learning | Support vector machines | Attributions | Forests | Algorithms | Discrepancies | Statistical analysis | Neural networks | Machine learning | Regression

Black box | Surface plus noise | Ephemeral predictors | Random forests | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Learning | Support vector machines | Attributions | Forests | Algorithms | Discrepancies | Statistical analysis | Neural networks | Machine learning | Regression

Journal Article

Journal of the American Statistical Association, ISSN 1537-274X, 12/2011, Volume 106, Issue 496, pp. 1602 - 1614

We suppose that the statistician observes some large number of estimates z
i
, each with its own unobserved expectation parameter Î¼
i
. The largest few of the...

Empirical Bayes information | False discovery rates | Regret | James-Stein | Bayesian relevance | Winner's curse | Maximum likelihood estimation | Statistical variance | Histograms | Density estimation | Estimate reliability | Degrees of freedom | Theory and Methods | Bayes estimators | Selection bias | Unbiased estimators | Skewed distribution | James-stein | Empirical bayes information | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Bayesian statistical decision theory | false discovery rates | regret | winnerâ€™s curse | empirical Bayes information | Jamesâ€“Stein

Empirical Bayes information | False discovery rates | Regret | James-Stein | Bayesian relevance | Winner's curse | Maximum likelihood estimation | Statistical variance | Histograms | Density estimation | Estimate reliability | Degrees of freedom | Theory and Methods | Bayes estimators | Selection bias | Unbiased estimators | Skewed distribution | James-stein | Empirical bayes information | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Bayesian statistical decision theory | false discovery rates | regret | winnerâ€™s curse | empirical Bayes information | Jamesâ€“Stein

Journal Article

Statistical science, ISSN 0883-4237, 5/2003, Volume 18, Issue 2, pp. 268 - 281

Bradley Efron is Professor of Statistics and Biostatistics at Stanford University...

Awards | Empiricism | Inference | P values | Biology | Bayesian theories | Statistics | Frequentism | Physics | The Impact of the Bootstrap | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology

Awards | Empiricism | Inference | P values | Biology | Bayesian theories | Statistics | Frequentism | Physics | The Impact of the Bootstrap | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology

Journal Article

2015, Revised edition., Research report, ISBN 083309033X, Volume RR-740-1-DCR., xlvii, 243 pages

Book

The Annals of statistics, ISSN 0090-5364, 04/2004, Volume 32, Issue 2, pp. 407 - 499

The purpose of model selection algorithms such as All Subsets, Forward Selection and Backward Elimination is to choose a linear model on the basis of the same...

Regression coefficients | Degrees of freedom | Algorithms | Approximation | Linear regression | Least squares | Coordinate systems | Mathematical vectors | Diabetes | Modeling | Least Angle Regression | Boosting | Lasso | Coefficient paths | Variable selection | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | linear regression | coefficient paths | variable selection | boosting | 62J07

Regression coefficients | Degrees of freedom | Algorithms | Approximation | Linear regression | Least squares | Coordinate systems | Mathematical vectors | Diabetes | Modeling | Least Angle Regression | Boosting | Lasso | Coefficient paths | Variable selection | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | linear regression | coefficient paths | variable selection | boosting | 62J07

Journal Article

Science (American Association for the Advancement of Science), ISSN 1095-9203, 06/2013, Volume 340, Issue 6137, pp. 1177 - 1178

The term "controversial theorem" sounds like an oxymoron, but Bayes' theorem has played this part for two-and-a-half centuries. Twice it has soared to...

Scientific method | Mathematical theorems | Logical theorems | Statistical theories | PERSPECTIVES | Twins | Statistics | Bayes theorem | Empirical evidence | Science & Technology - Other Topics | Multidisciplinary Sciences | Science & Technology | Science | Theorems | Boom | Reasoning | Inference | Landmarks | Acoustics | Bayesian analysis

Scientific method | Mathematical theorems | Logical theorems | Statistical theories | PERSPECTIVES | Twins | Statistics | Bayes theorem | Empirical evidence | Science & Technology - Other Topics | Multidisciplinary Sciences | Science & Technology | Science | Theorems | Boom | Reasoning | Inference | Landmarks | Acoustics | Bayesian analysis

Journal Article