The Wharton School
Professor of Statistics

Professor Wyner received his Bachelors degrees in Mathematics from Yale University, where he graduated Magna Cum Laude with distinction in his major. He was the recipient of the Stanley Prize for excellence in Mathematics. His PhD in Statistics is from Stanford University, where he won a National Science Foundation Graduate Fellowship, the Abrams Prize and the Herz Foundation fellowship. After graduating from Stanford, he received the NSF postgraduate fellowship and a visiting Professorship at the University of California, Berkeley. Dr. Wyner has been a Professor of Statistics at the Wharton School of Business for the last 11 years. He is a tenured Professor and the Chair of the Undergraduate Program in Statistics for the University of Pennsylvania.

Professor Wyner is an expert at Probability Models and Statistics. His principle focus at Wharton has been research in Applied Probability, Information Theory and Statistical Learning. He has published more than 30 articles in leading journals in many different fields, including Applied Statistics, Applied Probability, Finance, Information Theory, Computer Science and BioInformatics. He has received grants from the NSF, NIH and private industry. Professor Wyner has participated in numerous consulting projects in various businesses. He was one the earliest consultants for TiVo, Inc, where he helped to develop early personalization software. Dr. Wyner created some of the first online data summarization tools, while acting as CTO for Surfnotes, Inc. More recently, he has developed statistical analyses for banks and marketing research firms and has served as consultant to several law firms in Philadelphia, New York and Washington, D.C. In addition, he has served as statistical faculty advisor for the University Pennsylvania Law School. His interest in sports statistics has led to a collaboration with ESPN where Dr. Wyner was the PI on the ESPN funded MLB player evaluation research project. He has worked has also served as a statistical expert for hedge funds and private equity concerns.

Philip A. Ernst, Larry Shepp, Abraham J. Wyner (2017), Yule's "Nonsense Correlation" Solved!, The Annals of Statistics, In press.

Abraham J. Wyner, Matthew Olson, Justin Bleich, David Mease (Under Revision), Explaining the Success of AdaBoost and Random Forests as Interpolating Classifiers.

Blakely McShane, Shane T. Jensen, Allan Pack, Abraham J. Wyner, Statistical Learning With Time Series Dependence: An Application to Scoring Sleep in Mice. Discussion paper with rejoinder , Journal of American Statistical Association, 108, pp. 11471172.

Abstract: We develop methodology that combines statistical learning methods with generalized Markov models, thereby enhancing the former to account for time series dependence. Our methodology can accommodate very general and very longterm time dependence structures in an easily estimable and computationally tractable fashion. We apply our methodology to the scoring of sleep behavior in mice. As methods currently used to score sleep in mice are expensive, invasive, and labor intensive, there is considerable interest in developing highthroughput automated systems which would allow many mice to be scored cheaply and quickly. Previous efforts at automation have been able to differentiate sleep from wakefulness, but they are unable to differentiate the rare and important state of rapid eye movement (REM) sleep from nonREM sleep. Key difficulties in detecting REM are that (i) REM is much rarer than nonREM and wakefulness, (ii) REM looks similar to nonREM in terms of the observed covariates, (iii) the data are noisy, and (iv) the data contain strong time dependence structures crucial for differentiating REM from nonREM. Our new approach (i) shows improved differentiation of REM from nonREM sleep and (ii) accurately estimates aggregate quantities of sleep in our application to videobased sleep scoring of mice. Supplementary materials for this article are available online.

Mathieu Wimmer, Justin Rising, Raymond Galante, Abraham J. Wyne, Allan Pack, Ted Abel (2013), **[Aging in Mice Reduces the Ability to Sustain Sleep/Wake States.

Abstract: One of the most significant problems facing older individuals is difficulty staying asleep at night and awake during the day. Understanding the mechanisms by which the regulation of sleep/wake goes awry with age is a critical step in identifying novel therapeutic strategies to improve quality of life for the elderly. We measured wake, nonrapid eye movement (NREM) and rapideye movement (REM) sleep in young (2–4 monthsold) and aged (22–24 monthsold) C57BL6/NIA mice. We used both conventional measures (i.e., bout number and bout duration) and an innovative spikeandslab statistical approach to characterize agerelated fragmentation of sleep/wake. The short (spike) and long (slab) components of the spikeandslab mixture model capture the distribution of bouts for each behavioral state in mice. Using this novel analytical approach, we found that aged animals are less able to sustain long episodes of wakefulness or NREM sleep. Additionally, spectral analysis of EEG recordings revealed that aging slows theta peak frequency, a correlate of arousal. These combined analyses provide a window into the mechanisms underlying the destabilization of long periods of sleep and wake and reduced vigilance that develop with aging.

Robert J Driver, Annesia L Lamb, Abraham J. Wyner, pp. 501506.

FY Hu, GM Hanna, W Han, F Mardini, SA Thomas, Abraham J. Wyner, pp. 10061017.

Justin Rising and Abraham J. Wyner, Partial Kelly Portfolios and Shrinkage Estimators , IEEE International Symposium on Information Theory Proceedings.

N. Naidoo, M Ferber, R.J. Galante, B.B. McShane, J.H. Hu, J Zimmerman, G Maislin, J Cater, Abraham J. Wyner, Role of Homer Proteins in the Maintenance of SleepWake States , PLoS ONE Genetics, 7.

B.B. McShane, R.J. Galante, M. Biber, Shane T. Jensen, Abraham J. Wyner, A.I. Pack (2012), [Assessing REM sleep in mice using video data, Sleep, 35.

Jeremy Pick, Yihan Chen, Jason T Moore, Yi Sun, Abraham J. Wyner, pp. 702712.

Past Courses


Data summaries and descriptive statistics; introduction to a statistical computer package; Probability: distributions, expectation, variance, covariance, portfolios, central limit theorem; statistical inference of univariate data; Statistical inference for bivariate data: inference for intrinsically linear simple regression models. This course will have a business focus, but is not inappropriate for students in the college.


Introduction to concepts in probability. Basic statistical inference procedures of estimation, confidence intervals and hypothesis testing directed towards applications in science and medicine. The use of the JMP statistical package.


Discrete and continuous sample spaces and probability; random variables, distributions, independence; expectation and generating functions; Markov chains and recurrence theory.


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.


This seminar will be taken by doctoral candidates after the completion of most of their coursework. Topics vary from year to year and are chosen from advance probability, statistical inference, robust methods, and decision theory with principal emphasis on applications.

Mathematical Sciences PostDoctoral Fellow, NSF, 1995

Penn Professors Findings Contradict Clemens’ Analysis of Career Stats, ESPN 02/10/2008

Knowledge @ Wharton

  • Skill or Luck? That’s the Key Question for FanDuel and DraftKings, Knowledge @ Wharton 11/13/2015
  • Books for the Beach, Knowledge @ Wharton 06/25/2013
  • Sports by the Numbers: Predicting Winners and Losers, Knowledge @ Wharton 04/20/2012
  • The Use — and Misuse — of Statistics: How and Why Numbers Are So Easily Manipulated, Knowledge @ Wharton 04/02/2008
  • Polling the Polling Experts: How Accurate and Useful Are Polls These Days?, Knowledge @ Wharton 11/14/2007
  • Has Major League Baseball Hit a Foul in Its Recent Skirmish with Online Fantasy Leagues?, Knowledge @ Wharton 06/14/2006
  • How Credible Are Polls? Is There a Better Way to Predict Outcomes in Politics and Business, Knowledge @ Wharton 11/03/2004

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