Theoretical statistics

Theoretical statistics
The theoretical research interests of the department focus on the mathematical foundations of data analysis, including time series analysis, pattern recognition and classification, nonparametric methods, survival analysis, information theory, asymptotic approximations, experimental design, causal inference, and graphical models for complex dependencies.
Methods for high dimensional data and machine learning
Faculty associated with the Designated Emphasis in Communication, Computation and Statistics work in this area. Peter Bartlett, Peter Bickel and Bin Yu have been working on theoretical analyses of "boosting" from both the statistics and computer science point of view. Michael Jordan and Martin Wainwright have been working on the construction of effective algorithms. Noureddine El Karoui and Peter Bickel are working on the asymptotic behavior of empirical covariance matrices as dimension and sample size becomes large. Juliet Shaffer works on multiple testing such as the False Discovery Rate.
Causal and graphical models
Mark van der Laan has recently published a book (with J. Robins) on causal modelling. Michael Jordan is completing a major treatise on graphical modelling. Martin Wainwright is working on the analysis of the Junction Tree Algorithm.
Time Series and Survival Analysis
David Brillinger has long worked on general modelling and analysis methods for time series as well as modifying the models effectively for applications in many fields, most recently environmental science and neuroscience. John Rice works on the theory and methods for analysis of data represented as functions with a view towards various applications. Nicholas Jewell and Mark van der Laan work on the modelling of complex types of data arising in clinical trials.
Classical Statistics
Ching Shui Cheng works on the deep algebraic and combinatorial aspects of experimental design. Leo Goodman works on methods for the analysis of discrete data such as the relation between log linear latent variable models and correspondence analysis. Philip Stark works on minimax problems in decision theory. Deborah Nolan works on empirical process theory. David Freedman and Peter Bickel have helped develop the theory of the bootstrap. Freedman has made significant contributions to the analysis of Bayes' procedures in high dimensional spaces.
Demographics and Phylogenetics
Kenneth Wachter works on demographic models, particularly biodemography, and the study of ageing. Stephen Evans works on models in phylogenetics and population genetics.
Information Theory
Bin Yu and Martin Wainwright work on the functions of statistics and information theory, such as Rissmen's MDL model selection method.
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