Research Interests: hierarchical modeling, model uncertainty, shrinkage estimation, treed modeling, variable selection, wavelet regression
PhD, Stanford University, 1981
MS, SUNY at Stony Brook, 1976
AB, Cornell University, 1972
Elected Fellow of the International Society for Bayesian Analysis (2014); Elected Fellow of the American Statistical Association (1997); Elected Fellow of the Institute of Mathematical Statistics (1995).
CBA Foundation Award for Outstanding Research Contributions (1998) and the CBA Foundation Award for Research Excellence (1995), The University of Texas at Austin.
Excellence in Education Award (2001) and the Joe D. Beasley Award for Teaching Excellence (1996), The University of Texas at Austin
McKinsey Award for Excellence in Teaching (1987) and the Emory Williams Award for Excellence in Teaching (1987), The University of Chicago.
Wharton: 2001-present (Chairperson, Statistics Department, 2008-2014; named Universal Furniture Professor, 2002)
Previous appointment: University of Texas at Austin, University of Chicago.
Visiting Appointments: Cambridge University; University of Paris; University of Valencia
Editor, Annals of Statistics, 2016-2018; Executive Editor, Statistical Science, 2004-2007.
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Abstract: For the last two decades, high-dimensional data and methods have proliferated throughout the literature. The classical technique of linear regression, however, has not lost its touch in applications. Most high-dimensional estimation techniques can be seen as variable selection tools which lead to a smaller set of variables where classical linear regression technique applies. In this paper, we prove estimation error and linear representation bounds for the linear regression estimator uniformly over (many) subsets of variables. Based on deterministic inequalities, our results provide “good” rates when applied to both independent and dependent data. These results are useful in correctly interpreting the linear regression estimator obtained after exploring the data and also in post model-selection inference. All the results are derived under no model assumptions and are non-asymptotic in nature.
Andreas Buja, Richard A. Berk, Lawrence D. Brown, Edward I. George, Emil Pitkin, Mikhail Traskin, Linda Zhao, Kai Zhang (2017), Models as Approximations, Part I: A Conspiracy of Nonlinearity and Random Regressors in Linear Regression, Statistical Science, (revision submitted).
Matthew T. Pratola, Hugh A. Chipman, Edward I. George, Robert E. McCulloch (Under Review), Heteroscedastic BART Using Multiplicative Regression Trees.
Abstract: This paper provides multiple approaches to perform valid post-selection inference in an assumption-lean regression analysis. To the best of our knowledge, this is the first work that provides valid post-selection inference for regression analysis in such a general settings that include independent, m-dependent random variables.
Edward I. George, Veronika Rockova, Paul R. Rosenbaum, Ville Satopää, Jeffrey H. Silber (2017), Mortality Rate Estimation and Standardization for Public Reporting: Medicare's Hospital Compare, Journal of the American Statistical Association, Applications, (in press).
Abstract: Bayesian models are increasingly fit to large administrative data sets and then used to make individualized recommendations. In particular, Medicare's Hospital Compare webpage provides information to patients about specific hospital mortality rates for a heart attack or Acute Myocardial Infarction (AMI). Hospital Compare's current recommendations are based on a random-effects logit model with a random hospital indicator and patient risk factors. Except for the largest hospitals, these individual recommendations or predictions are not checkable against data, because data from smaller hospitals are too limited to provide a meaningful check. Before individualized Bayesian recommendations, people derived general advice from empirical studies of many hospitals; e.g., prefer hospitals of type 1 to type 2 because the risk is lower at type 1 hospitals. Here we calibrate these Bayesian recommendation systems by checking, out of sample, whether their predictions aggregate to give correct general advice derived from another sample. This process of calibrating individualized predictions against general empirical advice leads to substantial revisions in the Hospital Compare model for AMI mortality. In order to make appropriately calibrated predictions, our revised models incorporate information about hospital volume, nursing staff, medical residents, and the hospital's ability to perform cardiovascular procedures. For the ultimate purpose of comparisons, hospital mortality rates must be standardized to adjust for patient mix variation across hospitals. We find that indirect standardization, as currently used by Hospital Compare, fails to adequately control for differences in patient risk factors and systematically underestimates mortality rates at the low volume hospitals. To provide good control and correctly calibrated rates, we propose direct standardization instead.
Daniel McCarthy, Kai Zhang, Lawrence D. Brown, Richard A. Berk, Andreas Buja, Edward I. George, Linda Zhao (2017), Calibrated Percentile Double Bootstrap For Robust Linear Regression Inference, Statistica Sinica, (in press).
Veronika Rockova and Edward I. George (2017), Fast Bayesian Factor Analysis via Automatic Rotations to Sparsity, Journal of the American Statistical Association, Theory and Methods, 111, pp. 1608-1622.
Abstract: Rotational transformations have traditionally played a key role in enhancing the interpretability of factor analysis via post-hoc modifications of the factor model orientation. Regularization methods also serve to achieve this goal by prioritizing sparse loading matrices. In this work, we cross-fertilize these two paradigms within a unifying Bayesian framework. Our approach deploys intermediate factor rotations throughout the learning process, greatly enhancing the effectiveness of sparsity inducing priors. These automatic rotations to sparsity are embedded within a PXL-EM algorithm, a Bayesian variant of parameter-expanded EM for posterior mode detection. By iterating between soft-thresholding of small factor loadings and transformations of the factor basis, we obtain (a) dramatic accelerations, (b) robustness against poor initializations and (c) better oriented sparse solutions. For accurate recovery of factor loadings, we deploy a two-component refinement of the Laplace prior, the spike-and-slab LASSO prior. The potential of the proposed procedure is demonstrated on both simulated and real high-dimensional data, which would render posterior simulation impractical.
Andreas Buja, Richard A. Berk, Lawrence D. Brown, Edward I. George, Arun Kumar Kuchibhotla, Linda Zhao (2016), Models as Approximations, Part II: A General Theory of Model-Robust Regression, Statistical Science, (submitted).
This course provides the fundamental methods of statistical analysis, the art and science if extracting information from data. The course will begin with a focus on the basic elements of exploratory data analysis, probability theory and statistical inference. With this as a foundation, it will proceed to explore the use of the key statistical methodology known as regression analysis for solving business problems, such as the prediction of future sales and the response of the market to price changes. The use of regression diagnostics and various graphical displays supplement the basic numerical summaries and provides insight into the validity of the models. Specific important topics covered include least squares estimation, residuals and outliers, tests and confidence intervals, correlation and autocorrelation, collinearity, and randomization. The presentation relies upon computer software for most of the needed calculations, and the resulting style focuses on construction of models, interpretation of results, and critical evaluation of assumptions.
STAT 621 is intended for students with recent, practical knowledge of the use of regression analysis in the context of business applications. This course covers the material of STAT 613, but omits the foundations to focus on regression modeling. The course reviews statistical hypothesis testing and confidence intervals for the sake of standardizing terminology and introducing software, and then moves into regression modeling. The pace presumes recent exposure to both the theory and practice of regression and will not be accommodating to students who have not seen or used these methods previously. The interpretation of regression models within the context of applications will be stressed, presuming knowledge of the underlying assumptions and derivations. The scope of regression modeling that is covered includes multiple regression analysis with categorical effects, regression diagnostic procedures, interactions, and time series structure. The presentation of the course relies on computer software that will be introduced in the initial lectures.
It’s a Wonderful Life is a Christmas classic, but Wharton statistics professor Edward George says it should also be required viewing for business leaders.Knowledge @ Wharton - 2013/04/8