Statistics

Faculty Research Summaries | Chairman's Introduction

Yali Amit

My research interests are in the following areas: 1) Computer vision, image analysis and speech recognition; 2) Object detection, recognition and model registration algorithms in digital images and acoustic data using hierarchies of templates; 3) Applications to optical character recognition, zip code reading, face detection and recognition, automatic anatomy identification in medical images, detection and recognition of acoustic signals. I emphasize computational efficiency.

Linda Brant Collins

I am interested in the applications of probability to insurance and finance, especially in the areas of reinsurance, enterprise risk management and practical actuarial methods. I also have interest in issues related to the teaching of statistics and actuarial mathematics and the training of new statistics teachers.

Mathias Drton

I am interested in graphical Markov models as well as in the application of algebraic techniques in statistics (algebraic statistics). Recent projects are concerned with:

Lars Peter Hansen

My research interests include time series econometrics, quantitative analysis of dynamic equilibrium models, and asset pricing.

Nina Hinrichs

My primary research interests are in the fields of computational biology and bioinformatics. I am currently focusing on applying statistical machine learning techniques to understand experimental data and simulation data of the kinetics of various molecular processes.

Steven P. Lalley

My research interests are in probability and random processes, in particular stochastic interacting systems, random walk, percolation, branching processes, combinatorial probability, ergodic theory, and connections between probability and geometry.

Gregory Lawler

My research interests are in random walks; Brownian motion and applications to lattice models in statistical physics, e.g., self-avoiding walks and other walks with strong interactions; and the use of conformal invariance in studying critical phenomena.

Peter McCullagh

The following is a list of my research interests: Linear and generalized linear models, exponential families; Asymptotic approximation to the distribution of estimators; Variance components and structured covariance models; Spatial models in agricultural applications, particularly models that are closed under conformal transformation; Category theory and projective systems: stochastic processes and regression processes; Representation-theory for normal categories: Linear models, factorial models, and homologous factors; Random objects: sequences, subsets, partitions, trees, arrays, matrices; Notions of exchangeability and partial exchangeability; Relation to categories; Foundations of statistical models: Functorial definition; Monte-Carlo integration as an application of a statistical model.

Mary Sara McPeek

I investigate applications of probability and statistics to genetics. This includes linkage disequilibrium and association mapping, modeling of background linkage disequilibrium, robust linkage analysis using affected pedigree members, detection of pedigree errors, physical map assembly and assessment of quality of the assembled map, counting-process models for genetic recombination, analysis of genomic rearrangements, homozygosity mapping of quantitative trait loci, estimation of genetic maps, analysis of single-sperm data, variance components methods for QTL mapping in a founder population, case-control association testing and Hardy-Weinberg testing in founder populations.

Debashis Mondal

I have a wide range of interests in Statistics including wavelet analysis in time series and random fields with applications in atmospheric sciences, central limit theorems, robust estimation, self--similar processes, geostatistics, Markov random fields, Markov chain Monte Carlo (MCMC). I also study the application of spatial statistics in agriculture, environmental science and other disciplines.

Per Mykland

My research interests are concerned with the analysis of longitudinal data, in particular survival analysis and inference in time series and diffusions. The latter is with main application to finance. I use likelihood and high frequency based methods.

In finance and economics, I investigate particular pricing and hedging of derivative securities. I study risk management and government regulation, and the interface between statistical uncertainty and prices, especially how to hedge against statistical uncertainty.

Other topics I study are: the application of likelihood theory to martingales, and vice versa; nonparametric likelihood; methods for analyzing and improving on asymptotic approximations to sampling distributions, including likelihood methods, asymptotic expansions (Edgeworth, saddlepoint) and resampling (bootstrapping, jackknifing); and stochastic simulation.

Dan Nicolae

My major research interests are in the areas of statistical genetics and mathematical statistics. The problems I am studying are mainly motivated by applications to the genetics of complex diseases.

Statistical genetics problems of interest include likelihood applications to gene mapping, multi-locus models and testing for gene-environment interaction, linkage disequilibrium and fine mapping, methods for genome-wide association studies, measures of relative information in genetic studies.

The applications I work on focus on finding the genetic and environmental components of asthma and the inflammatory bowel disease. I am also interested in functional genomics and the analysis of gene expression data.

Mathematical statistics topics I am working on include Bayesian and frequentist ways of measuring the amount of missing data, artificial likelihoods in hypothesis testing, and Monte-Carlo integration.

Partha Niyogi

I am broadly interested in the problem of human and machine intelligence. To make progress, I examine this with the point of view provided by the twin windows of learning and language. In many ways, learning is the centerpiece of intelligence. This is what presumably distinguishes "intelligent'' from "pre-programmed'' behavior. Language is partly interesting because it is almost certainly learnt. Together they provide a testbed of challenging problems that shed insight on the nature of intelligence and if successful would lead to significant applications of the future. My specific research program therefore focuses on learning and language - how each works in the human and how they can be replicated in a machine.

Michael Stein

My research focuses on statistical models and methods for spatial and spatial-temporal processes. In particular, I am interested in the nature of the spatial-temporal interactions implied by these models and on developing statistical methods for assessing these interactions. Some of the processes my collaborators and I are currently studying include stratospheric ozone, air pollution at both regional and urban scales, and sediment transport in the Great Lakes. One of our goals is to incorporate the information from deterministic physical models into the statistical modeling of these processes in order to evaluate and improve the physical models and to provide better predictions of spatial-temporal processes than can be obtained from either purely statistical or purely deterministic approaches.

Matthew Stephens

My general interests include Bayesian and computational statistics, particularly when applied to problems in population genetics. Specific interests include:

Stephen M. Stigler

I investigate of the history of the development of statistical methods, with attention to the different ways in which problems in astronomy, geodesy, social sciences, and psychology accelerated or inhibited this development. Topics include: the study of the reception of quantification in the sciences, from seventeenth-century medicine to twentieth-century social science, and of the way twentieth-century conceptual developments evolved from earlier work and advances in technology; the investigation of how understanding of regression and aggregation paradoxes have influenced policy debates, and how subtle mathematical developments in the twentieth century have become confounded with personal disputes and the formation of scientific schools; the history of lotteries in the 18th and 19th centuries and their role in forming (and reflection of) public attitudes towards risk; and twentieth century mathematical statistics, particularly the work and relationship between Karl Pearson and Ronald Fisher. Additional topics include: the application of statistical theory in such areas as the written transmission of historical information; the evaluation of trends, periodicities, and anomalies in the fossil record; clustering in cultural anthropology; the optimal arrangement of published information; the measurement of influence in scientific research; and the statistics of sports, particularly in baseball and tournament golf.

Ronald A. Thisted

My major research interests are in the areas of biostatistics and epidemiology, statistical computation, and health-services research.

In biostatistics/epidemiology, I am studying regression methods for paired data with ordered categorical outcomes, problems of multiple inference in clinical trials, methods for combining information (meta-analysis), concerning diagnostic tests such as those used in nuclear medicine, and assessment of causal relationships associated with rare but catastrophic events such as sudden death in children.

My current work in statistical computation includes data structures for bibliographic data bases, electronic publishing, computational aspects of meta-analysis, and improved design of Monte Carlo studies.

Current efforts in health-services research include comparative assessment of outcomes for men with prostate cancer treated by different therapies, assessment of effectiveness for prostate-specific antigen tests for screening, diagnosis, and follow-up of prostate cancer, short- and long-term effectiveness of treatments for degenerative disease of the lumbar spine, and relative benefits of SPECT imaging relative to standard diagnostics in epilepsy and dementia.

Mei Wang

My research focuses on probabilistic-mathematical models and related statistical methods with applications in biological sciences. In particular, I am interested in models that require mathematical and probabilistic formulation to describe biological mechanisms. I am also into certain mathematical aspects of theoretical statistics and probability. The following are the topics that I have worked on recently. In addition, I am generally interested in environmental statistics and some of the challenges in statistical modeling by large datasets.

Michael J Wichura

I study first and last crossing distributions of moving boundaries by stochastic processes, utilizing both theoretical and numerical techniques. I also study convergence rates for laws of large numbers.

Kirk Wolter

Kirk Wolter served as NORC's Senior Vice President of Statistics and Methodology for eight years and now heads up the new Center for Excellence in Survey Research. He is also Professor, Department of Statistics, University of Chicago. During his career, he has led or participated in the design of many of America's largest and most important information systems, including the Current Business Surveys, the Current Employment Statistics program, the Current Population Survey, the 1980 and 1990 Decennial Censuses, the National Longitudinal Survey of Youth 1997, and the National Resources Inventory. He led the conversion of major market research surveys to scanning-based methods of data collection, both in American and in many of the countries in Western Europe. He currently works with the Centers for Disease Control and Prevention to conduct the National Immunization Survey, a study of childhood immunization and one of the world's largest RDD (random digit dialing) telephone survey.

Wei-Biao Wu

In the study of random processes, dependence plays a fundamental role. By interpreting random processes as physical systems, I introduce physical dependence coefficients that quantify the degree of dependence of outputs on inputs. Such dependence measures are related to the nonlinear system theory and riskmetrics. They provide a new framework for the study of random processes and shed new light on a variety of problems including estimation of linear models with dependent errors, nonparametric inference of time series, representations of sample quantiles, bootstrap for time series, spectral estimation among others. This work is published at Wu (October, 2005): “Nonlinear system theory: Another look at dependence,” Proceedings of the National Academy of Sciences. I am currently interested in estimating covariance matrices of temporally observed series. The latter problem is quite important in the study of functional and longitudinal data. On the other hand, however, this problem is notoriously difficult since (i) one needs to estimate as many as n(n+1)/2 unknowns for a covariance matrix and (ii) a covariance matrix is intrinsically positive definite if the underlying random vector is linearly independent. This work is joint with Mohsen Pourahmadi.