
Robert L. Wolpert, Professor of Statistical Science and Professor in the Division of Environmental Sciences and Policy
I'm a stochastic modeler I build computerresident mathematical models for complex systems, and invent and program numerical algorithms for making inference from the models. Usually this involves predicting things that haven't been measured (yet). Always it involves managing uncertainty and making good decisions when some of the information we'd need to be fully comfortable in our decisionmaking is unknown.
Originally trained as a mathematician specializing in probability theory and stochastic processes, I was drawn to statistics by the interplay between theoretical and applied research with new applications suggesting what statistical areas need theoretical development, and advances in theory and methodology suggesting what applications were becoming practical and so interesting. Through all of my statistical interests (theoretical, applied, and methodological) runs the unifying theme of the <STRONG>Likelihood Principle</STRONG>, a constant aid in the search for sensible methods of inference in complex statistical problems where commonlyused methods seem unsuitable. Three specific examples of such areas are:
* Computer modeling, the construction and analysis of fast small Bayesian statistical emulators for big slow simulation models; * Metaanalysis, of how we can synthesize evidence of different sorts about a statistical problem; and * Nonparametric Bayesian analysis, for applications in which common parametric families of distributions seem unsuitable.
Many of the methods in common use in each of these areas are hard or impossible to justify, and can lead to very odd inferences that seem to misrepresent the statistical evidence. Many of the newer approaches abandon the ``iid'' paradigm in order to reflect patterns of regional variation, and abandon familiar (e.g. Gaussian) distributions in order to reflect the heavier tails observed in realistic data, and nearly all of them depend on recent advances in the power of computer hardware and algorithms, leading to three other areas of interest:
* Spatial Statistics, * Statistical Extremes, and * Statistical computation.
I have a special interest in developing statistical methods for application to problems in Environmental Science, where traditional methods often fail. Recent examples include developing new and better ways to estimate the mortality to birds and bats from encounters with wind turbines; the development of nonexchangeable hierarchical Bayesian models for synthesizing evidence about the health effects of environmental pollutants; and the use of highdimensional Bayesian models to reflect uncertainty in mechanistic environmental simulation models. <P> My current (20152016) research involves modelling and Bayesian inference of dependent time series and (continuoustime) stochastic processes with jumps (examples include work loads on networks of digital devices; peak heights in mass spectrometry experiments; or multiple pollutant levels at spatially and temporally distributed sites), problems arising in astrophysics (Gamma ray bursts) and highenergy physics (heavy ion collisions), and the statistical modelling of risk from, e.g., volcanic eruption.
 Contact Info:
 Office Hours:
 Vary from term to term. Check course website.
 Education:
Ph.D.  Princeton University  1976 
B.A.  Cornell University  1972 
AB  Cornell University  1972 
 Specialties:

Statistical Modeling
statistics Bayesian Statistics ecology Stochastic Processes environmental toxicology Spatial Statistics
 Research Interests: Nonparametric Bayesian Models, Stochastic Processes & Time Series, and Spatial Statistics
 Areas of Interest:
Spatial statistics Stochastic Processes, Stochastic Analysis Nonparametric Bayesian analysis Modeling & Decision Support in Complex Systems Environmental & Epidemiological Applications
 Keywords:
Bayes Theorem • Computer Simulation • Crisis Intervention • Decision Support Techniques • Environmental Monitoring • MetaAnalysis as Topic • Models, Biological • Models, Statistical • Models, Theoretical • Ozone • Probability • Rats, Inbred Strains • Rheology • Risk • Rivers • Taste • Toxicology • Transportation • Water Microbiology
 Current Ph.D. Students
(Former Students)
 Natesh Pillai
 Chong Tu
 Jingqin '. Luo
 Gangqiang Xia
 Casey Lichtendahl
 Dawn Banard
 Zhenglei Gao
 Leanna House
 Joe Lucas
 Floyd Bullard
 Representative Publications
(More Publications)
 Dominici, F; Parmigiani, G; Reckhow, KH; Wolpert, RL, Combining Information from Related Regressions,
Journal of Agricultural, Biological, and Environmental Statistics, vol. 2 no. 3
(January, 1997),
pp. 313332, Springer Nature, ISSN 10857117 [doi] [abs]
 James O. Berger and Robert L. Wolpert, The Likelihood Principle: A Review, Generalizations, and Statistical Implications (with discussion), IMS Lecture NotesMonograph Series, vol. 6
(1988), Institute of Mathematical Statistics, Hayward, CA
 Wolpert, RL; Taqqu, MS, Fractional OrnsteinUhlenbeck Lévy processes and the Telecom process: Upstairs and downstairs,
Signal Processing, vol. 85 no. 8
(August, 2005),
pp. 15231545, Elsevier BV [doi] [abs]
 Dominici, F; Parmigiani, G; Wolpert, RL; Hasselblad, V, MetaAnalysis of Migraine Headache Treatments: Combining Information from Heterogeneous Designs,
Journal of the American Statistical Association, vol. 94 no. 445
(March, 1999),
pp. 1628, ISSN 01621459 [doi] [abs]
 Wolpert, RL; Mengersen, KL, Adjusted likelihoods for synthesizing empirical evidence from studies that differ in quality and design: Effects of environmental tobacco smoke,
Statistical Science, vol. 19 no. 3
(August, 2004),
pp. 450471, Institute of Mathematical Statistics [doi] [abs]
 Wolpert, RL; Ickstadt, K, Reflecting uncertainty in inverse problems: A Bayesian solution using Lévy processes,
Inverse Problems, vol. 20 no. 6
(December, 2004),
pp. 17591771, IOP Publishing, ISSN 02665611 [doi] [abs]
 Wolpert, RL, Invited discussion of `On the Probability of Observing Misleading Statistical Evidence', by R. Royall,
J. American Statistical Assoc., vol. 95 no. 451
(2000),
pp. 771772
 N.G. Best, K. Ickstadt & R.L. Wolpert, Spatial Poisson regression for health and exposure data measured at disparate spatial scales,
J. American Statistical Assoc., vol. 95 no. 452
(2000),
pp. 10761088
 Lavine, M; Wasserman, L; Wolpert, RL, Bayesian inference with specified prior marginals,
Journal of the American Statistical Association, vol. 86 no. 416
(January, 1991),
pp. 964971, JSTOR, ISSN 01621459 [Gateway.cgi], [doi] [abs]
 Robert L. Wolpert and Katja Ickstadt, Simulation of L\'evy Random Fields,
in Practical Nonparametric and Semiparametric Bayesian Statistics, Lecture Notes in Statistics, edited by Dipak K. Dey and Peter M\^^buller and Debajyoti Sinha, vol. 133
(1998),
pp. 227242, SpringerVerlag, New York, NY, ISBN 0387985174
 Wolpert, RL; Ickstadt, K, Poisson/gamma random field models for spatial statistics,
Biometrika, vol. 85 no. 2
(January, 1998),
pp. 251267, Oxford University Press (OUP), ISSN 00063444 [doi] [abs]
 Best, NG; Ickstadt, K; Wolpert, RL, Spatial Poisson Regression for Health and Exposure Data Measured at Disparate Resolutions,
Journal of the American Statistical Association, vol. 95 no. 452
(December, 2000),
pp. 10761088, Informa UK Limited, ISSN 01621459 [doi] [abs]
 Berger, JO; Brown, LD; Wolpert, RL, A Unified Conditional Frequentist and Bayesian Test for Fixed and Sequential Simple Hypothesis Testing,
The Annals of Statistics, vol. 22 no. 4
(December, 1994),
pp. 17871807, Institute of Mathematical Statistics, ISSN 00905364 [Gateway.cgi], [doi]
 Berger, JO; Liseo, B; Wolpert, RL, Integrated likelihood methods for eliminating nuisance parameters,
Statistical Science, vol. 14 no. 1
(January, 1999),
pp. 122, Institute of Mathematical Statistics [doi] [abs]
