Duke Probability Theory and Applications
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The Duke probability group is a collection of faculty spanning the different divisions of the university who are interested in probability theory and the application of stochastic modeling.

The group runs a weekly seminar which loosely alternates between the theory and applications of probability and stochastic modeling. If you are interested in getting email about stochastic happenings at Duke, please subscribe to our mailing list.

Members:     List alphabetically  by specialties  photos
  • Richard T. Durrett, James B. Duke Professor and Director of Graduate Studies, (primary appt: Mathematics)
  • Otis B. Jennings, Adjunct Associate Professor (primary appt: Fuqua School of Business)
  • Shakeeb Khan, Professor (primary appt: Economics)

    Professor Khan specializes in the fields of mathematical economics, statistics, and applied econometrics. His studies have explored a variety of subjects from covariate dependent censoring and non-stationary panel data, to causal effects of education on wage inequality and the variables affecting infant mortality rates in Brazil. He was awarded funding by National Science Foundation grants for his projects entitled, “Estimation of Binary Choice and Nonparametric Censored Regression Models” and “Estimation of Cross-Sectional and Panel Data Duration Models with General Forms of Censoring.” He has published numerous papers in leading academic journals, including such writings as, “Heteroskedastic Transformation Models with Covariate Dependent Censoring” with E. Tamer and Y. Shin; “The Identification Power of Equilibrium in Simple Games;” “Partial Rank Estimation of Duration Models with General Forms of Censoring” with E. Tamer; and more. He is currently collaborating with D. Nekipelov and J.L. Powell on the project, “Optimal Point and Set Inference in Competing Risk Models;” with A. Lewbel on, “Identification and Estimation of Stochastic Frontier Models;” and with E. Tamer on, “Conditional Moment Inequalities in Roy Models with Cross-Section and Panel Data.”

  • Mauro Maggioni, Professor (primary appt: Mathematics and Electrical and Computer Engineering and Computer Science)

    I am interested in novel constructions inspired by classical harmonic analysis that allow to analyse the geometry of manifolds and graphs and functions on such structures. These constructions are motivated by several important applications across many fields. In many situations we are confronted with large amounts of apparently unstructured high-dimensional data. I find fascinating to study the intrinsic geometry of such data, and exploiting in order to study, explore, visualize, characterize statistical properties of the data. Oftentimes such data is modeled as a manifold (or something "close to a manifold") or a graph, and functions on these spaces need to approximated or "learned" from the data and experiments on the data. For example each data point could be a document, a graph associated with the documents could be given by for example hyperlinks, or by similarity of word frequencies, and a function on the set of documents would be how interesting I personally score a document. One may wish to learn how to predict how much I would score documents I have not seen yet. This can be cast as an approximation problem on the graph of documents, and it turns out that one can generalize Euclidean-type approximation techniques (in particular multiscale regression techniques) to tackle this problem. An application of the above techniques that I find particularly interesting is Markov Decision Processes and Reinforcement Learning, where the problem of learning a behaviour from experience is cast in a rather general optimization and learning framework that involves approximations of functions and operators on graphs and manifolds. I am also interested in imaging, in particular I am working on novel classes of nonlinear denoising algorithms, based on diffusion processes on graphs of features built from images. Another interest is in the geometry of multiscale dynamical systems, and the construction of algorithms for the empirical construction of approximate equations for such systems. I also work on hyperspectral imaging, in particular in building automatic classifiers for discriminating normal from cancerous biopsies, for automated diagnostics and pathology.

  • Jonathan C. Mattingly, Professor (primary appt: Mathematics)

    Test Overview.

  • Sayan Mukherjee, Professor (primary appt: Statistical Science and Computer Science)
  • James H. Nolen, Assistant Professor (primary appt: Mathematics)

    I study partial differential equations, which have been used to model many phenomena in the natural sciences and engineering. In many cases, the parameters for such equations are known only approximately, or they may have fluctuations that are best described statistically. So, I am especially interested in equations modeling random phenomena and whether one can describe the statistical properties of the solution to these equations. For example, I have worked on nonlinear partial differential equations that describe waves and moving interfaces in random media. This work involves ideas from both analysis and probability.

  • Dalia Patino-Echeverri, Gendell Assistant Professor of Energy Systems and Public Policy and Assistant Professor of Energy Systems and Public Policy in the Division and Faculty Network Member of Energy Initiative and Affiliate of the Duke Initiative for Science & Society, (primary appt: Environmental Sciences and Policy)

    Dr. Patino-Echeverri’s research focuses on public policy design for energy systems, with a particular emphasis on managing the risks arising from the uncertainties influencing the outcomes of government actions. Much of her current work focuses on the policies that affect capital investment decisions within the electricity industry, and the corresponding costs to society of electricity and air-emissions levels. Her models explore the effects of different government policies by representing the industry’s decisions under uncertainty on future technological advancements, fuel prices, and emissions regulations.

  • Amilcare Porporato, Addy Professor (primary appt: Civil and Environmental Engineering)

    Amilcare Porporato earned a Master Degree in Civil Engineering (summa cum laude) in 1992 and his Ph.D. in 1996 from Polytechnic of Turin. He was appointed Assistant Professor in the Department of Hydraulics of the Polytechnic of Turin, and he moved to Duke University in 2003, where he is now Full Professor in the Department of Civil and Environmental Engineering with a secondary appointment with the Nicholas School of the Environment.

    In June 1996, Porporato received the Arturo Parisatti International Price, awarded by the Istituto Veneto di Scienze, Lettere e Arti. He was Research Associate at the Texas A&M University (USA) in 1998 and Visiting Scholar at Princeton University (USA), Department of Civil and Environmental Engineering, from 1999 to 2001. In 2008-2009 he was the first Landolt & Cie Visiting Chair in “Innovative Strategies for a sustainable Future” at Ecole Polytechnique Federale de Lausanne (EPFL), Switzerland. He was awarded the 2007 Professor Senol Utku’ award, the 2010 Earl Brown II Outstanding Civil Engineering Faculty Award, and in 2011 he received a Lagrange fellowship from the Polytechnic of Turin, the CRT bank and the ISI (Institute for Scientific Interchange). In 2012 he was elected an AGU fellow.

    His main research interests regard nonlinear and stochastic dynamical systems, hydrometeorology and soil-atmosphere interaction, soil moisture and plant dynamics, soil biogeochemistry, and ecohydrology.

    Porporato has been Editor of Water Resources Research (AGU) (2004-2009), and he is currently editor for Hydrological Processes. He is also member of the editorial board of Advances in Water Resources and the Hydrologic Science Journal. Among other things, he was chairman and convener of the Ecohydrology sessions of the AGU Spring Meeting in 2001 and 2002 and of the EGU in 2004-2006. Porporato has been part of the Italian research groups of Turbulence and Vorticity and of Climate, Soil and Vegetation Interaction, an adviser for real-time forecasting in the Piedmont Region (Italy), and ecohydrology (US National Academy).

    Porporato's didactic experience comprises courses in Environmental Fluid Mechanics, Hydraulics, Hydraulic Constructions, Statistical and Physical Hydrology, Ecohydrology, Nonlinear Dynamics and Stochastic Processes. He has also been the didactic coordinator for the International School "Hydroaid: Water for Development", co-organized by the Polytechnic of Turin and the Italian Ministry of Foreign Affairs.

    Porporato is author of more than 140 peer-reviewed papers, several publications presented at national and international conferences and invited talks. He is also co-author of the book "Ecohydrology of water controlled ecosystems" (Cambridge Univ. Press, 2004) and the edited the book "Dryland Ecohydrology" (Springer, 2005).

  • Scott C. Schmidler, Associate Professor (primary appt: Statistical Science and Computer Science)
  • George E. Tauchen, William Henry Glasson Professor (primary appt: Economics)

    George Tauchen is the William Henry Glasson Professor of Economics and professor of finance at the Fuqua School of Business. He joined the Duke faculty in 1977 after receiving his Ph.D. from the University of Minnesota. He did his undergraduate work at the University of Wisconsin. Professor Tauchen is a fellow of the Econometric Society, the American Statistical Association, the Journal of Econometrics, and the Society for Financial Econometrics (SoFie). He is also the 2003 Duke University Scholar/Teacher of the Year. Professor Tauchen is an internationally known time series econometrician. He has developed several important new techniques for making statistical inference from financial time series data and for testing models of financial markets.  He has given invited lectures at many places around the world, including London, Paris, Beijing, Taipei, Hong Kong, and Sydney. His current research (with Professor Li of Duke) examines the impact of large jump-like moves in stock market returns on the returns of various portfolios and individual securities.  He is a former editor of the Journal of Business and Economic Statistics (JBES) and former associate editor of Econometrica, Econometric Theory, The Journal of the American Statistical Association (JASA), and JBES.   He is currently Co-Editor of the Journal of Financial Econometrics.

  • Surya Tokdar, Assistant Professor and Faculty Network Member of Duke Institute for Brain Sciences and Co-Director of Graduate Studies, (primary appt: Statistical Science)
  • Mike West, Arts and Sciences Professor of Statistics and Decision Sciences and Member of Duke Cancer Institute, (primary appt: Statistical Science)

    Go to my personal web page for links and info on my teaching, publication list (sortable and searchable -- just click on table headers), current research, current & past students, software, etc.

  • Robert L. Wolpert, Professor and Professor in the Division of Environmental Sciences and Policy, (primary appt: Statistical Science)

    I'm a stochastic modeler-- I build computer-resident 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 decision-making 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 commonly-used 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;
    * Meta-analysis, 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 high-dimensional Bayesian models to reflect uncertainty in
    mechanistic environmental simulation models. <P> My current (2015-2016)
    research involves modelling and Bayesian inference of dependent time series
    and (continuous-time) 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 high-energy physics (heavy ion collisions), and the statistical
    modelling of risk from, e.g., volcanic eruption.