Faculty Research Summaries | Chairman's Introduction

• Yali Amit, Associate Professor, Department of Statistics and the College
• Patrick Billingsley, Professor Emeritus, Departments of Mathematics and Statistics and the College
• Zhiyi Chi, Assistant Professor, Department of Statistics and the College
• William H. Kruskal, Ernest DeWitt Burton Distinguished Service Professor Emeritus, Department of Statistics and the College; Professor Emeritus, Harris Graduate School of Public Policy Studies
• Steven Lalley, Professor, Department of Statistics and the College
• Michael Larsen, Senior Lecturer, Department of Statistics and the College
• Peter McCullagh, Ralph and Mary Otis Isham Professor, Department of Statistics and the College
• Mary Sara McPeek, Assistant Professor, Department of Statistics and the College; Member of the Committee on Genetics
• Xiao-Li Meng, Associate Professor, Department of Statistics and the College
• Per Mykland, Associate Professor, Department of Statistics and the College
• Dan Nicolae, Assistant Professor, Department of Statistics and the College
• Michael L. Stein, Professor, Department of Statistics and the College; Chairman, Department of Statistics
• Stephen M. Stigler, Ernest DeWitt Burton Distinguished Service Professor, Department of Statistics and the College; Member of the Committee on Conceptual Foundations of Science
• Ronald A. Thisted, Professor, Departments of Anesthesia and Critical Care, Statistics and the College; Chairman, Department of Health Studies
• David L. Wallace, Professor Emeritus, Department of Statistics and the College
• Michael J. Wichura, Associate Professor, Department of Statistics and the College
• Kirk Wolter, Professor, Department of Statistics

Yali Amit

Computer vision and image analysis: Object detection, recognition and model registration algorithms in digital images and acoustic data using spatial graphical models. Applications to hand-written character recognition, zip code reading, face detection and recognition, automatic anatomy identification in medical images, and speech recognition. Computational efficiency is emphasized.

Statistical modeling and analysis of the data for understanding the performance. of the algorithms.

Parallel and biologically plausible neural architectures for implementing these algorithms. Interactions with research on primate vision.

Patrick Billingsley

Most effort has been devoted to limit theo-rems in probability, modern descendants of the central limit theorem. These have application to statistics as well as to Diophantine approxima-tion, the distribution of prime divisors, and other subjects in number theory. Also problems link-ing probability and Hausdorff dimension theory.

Zhiyi Chi

Various topics in probability, including self-similar random fields, branching processes, and large deviations.

Information theory. Statistical modeling in computational linguistcs, especially for sentence parsing. Image analysis using point processes.

William H. Kruskal

Statistics and public policy. Work on a vari-ety of problems on the boundary between theoret-ical statistics and public policy: census under-enumeration, confidentiality, evaluation proce-dures, etc.

History of statistics. Currently have several historical projects in hand. One, for example, deals with concepts of normality in statistics, medicine and elsewhere. Relative importance. Investigators often wish to describe the relative importance of two or more inputs to some kind of output (e. g., family background, school funding, and hours of study as they affect aca-demic achievement; pressure, temperature, and total time as they affect an industrial process.) Typically, ad hoc ways of measuring relative im-portance are used, and I would like to understand these measures at a more basic level.

Steven Lalley

My main interest currently is the behavior of stochastic processes in graphs with ``noneuclidean'' geometries, in particular, graphs with exponential with exponential volume growth. Various stochastic processes used as crude models of population growth, Including branching random walks and contact processes, exhibit drastically different behaviors in such graphs than those that are observed in graphs with polynomial growth, such as the regular Euclidean lattices. I am especially interested in the existence of a ``weak survival phase'' for such processes. In this phase, the ``population'' survives (and grows) with positive probability, but almost surely eventually vacates every finite subset of the graph. This phase does not occur in regular Euclidean lattices.

Percolation processes, which are of interest in statistical physics, also exhibit unusual behavior in graphs with exponential with exponential volume growth. There is an analogue of the weak survival phase, the ``coexistence phase'', in which there are, almost surely, infinitely many infinite connected clusters. The geometric properties of such clusters is of particular interest to me.

I have recently developed an interest in the analysis of time series data produced by nonlinear dynamical systems. The objective is to guess the dynamical laws governing the system from long time series of scalar measurements on it. Conventional methods of ``linear'' time series analysis are of limited usefulness here. Exploitation of the ergodic theory of nonlinear dynamical systems may, however, allow the development of suitable methods of analysis.

Michael Larsen

Finite mixture models applied in psychology and in government, specifically at the U.S. Bureau of the Census in record-linkage operations. Small-area estimation using hierarchical and empirical Bayesian methods with application to complex sample surveys about alcohol and drug use. Propensity score methods applied to sample surveys on tobacco use. Issues related to the U.S. Decennial Census, including non-response follow-up, statistical adjustment, imputation, and use of administrative records. Algorithms and models for use in incomplete-data problems. Model and variable selection.

Peter McCullagh

Models that are not quite linear, but have enough of a linear structure to be worth exploit-ing, are extremely common in applications. I have been interested in such generalized linear models, models having several components of error, associated computational issues, distributional problems, asymptotic approximations, and so on.

Frequency-theory inferential statements in the form of p-values or confidence intervals are the norm in practice, yet a wholly satisfactory foun-dation is missing. I have been studying the role of approximately ancillary statistics, and the ef-fect of the stopping rule, either via specific ex-amples or in an asymptotic context. These stud-ies lead to interesting connections with discrete mathematics, differential geometry, invariance, and group theory. But, thus far, no satisfactory foundation for frequency-theory inference.

Recently, I have developed and interest in the application of abstract algebra to statistics and statistical models. In particular, the structure of factorial models and analysis of variance is closely related to representation theory for the category of all maps on finite sets.

Mary Sara McPeek

Applications of probability and statistics to genetics. Counting-process models for genetic recombination, analysis of genomic rearrangements, heritability, pedigree error detection, estimation of genetic maps, analysis of single-sperm data, robust linkage analysis using affected relatives, assessment of linkage disequilibrium with application to genetic mapping, variance components methods for QTL mapping in humans.

Xiao-Li Meng

Incomplete-data analysis. Latent variable modeling. Inference with multiply-imputed data sets. Theory of model incompatibility and uncongeniality. Theory and methods for estimating relative information in the context of genetic studies.

Deterministic and stochastic methods for likelihood and Bayesian computation. Efficient Monte Carlo methods, including exact/perfect simulation. Theory of rate of convergences of iterative algorithms.

Bayesian model building and diagnostics. Frequentist properties of Bayesian methods. Hybrid inferences.

Trend detection. Environmental statistics.

Per Mykland

Analysis of longitudinal data, in particular survival analysis and inference in time series and differential equations, with application to finance. Stochastic simulation. Design of experiments. Observational studies.

Finance and economics, in particular pricing and hedging of derivative securities. Risk management. The interface between statistical uncertainty and prices, especially how to hedge against statistical uncertainty. Incomplete markets.

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).

Dan Nicolae

Statistical genetics: likelihood applications to gene mapping, measures of relative information, multi-locus models and testing for gene-gene interaction, linkage disequilibrium and fine mapping, finding mutations for IBD.

Likelihood theory: dual likelihood and missing information, bridge sampling and empirical likelihood.

Michael Stein

Spatial statistics. Prediction for spatial pro-cesses, especially of area averages. Spectral analysis of spatial and space-time data. A recur-rent theme in my work on spatial statistics is the exploration of different and sometimes nonstan-dard asymptotic regimes for studying the behav-ior of statistical procedures.

Applications of statistics to geophysics and environmental monitoring. Statistical inference for spatial point processes and its application in cosmology.

Stephen M. Stigler

Investigation 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. 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 role in understanding of regression and aggregation paradoxes have influences policy debates, and how subtle mathematical developments in the twentieth century have become confounded with personal disputes and the formation of scientific schools.

Investigation of properties of robust estimators, asymptotic theory for linear functions of order statistics, and conceptual bases for multiparameter inference, including the relationship between clustering problems and high dimensional linear estimation problems.

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, and the measurement of influence in scientific research.

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.

David L. Wallace

Study of principled methods of formal statistical inference, especially Bayesian, fiducial and likelihood-based methods, in relation to informal methods of exploratory data analysis. Find problems that display dissonance between the methods. Examples include Inference about uncertain constructs like ratios, directions and maxima, and misbehavior of the modified likelihood ratio test for comparing two means.

Contrast actual and expected performance of asymptotic approximations and develop guides for assessing adequacy of large-sample methods.

Michael J. Wichura

Study of first and last crossing distributions of moving boundaries by stochastic processes, utilizing both theoretical and numerical tech-niques. Convergence rates for laws of large numbers.

Kirk Wolter

Sample surveys; federal statistical policy; international statistics; marketing research; decennial census requirements and methods; census undercount; training for survey sampling/survey research.