Department Research Interests

The research of our department can be divided into three main areas: theoretical statistics, applied statistics, and probability. Within these areas, currently there are 27 faculty (of whom 7 work primarily in probability theory), 7 postdoctoral researchers, and 8 visiting faculty involved in various research projects. Here are summaries of the main areas of interest:

Specific Faculty Research Interests (Organized by Name)

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.

 

Applied Statistics

The information technology revolution has advanced data collection capacities in almost all fields of science, social science, engineering, and beyond. The resulting data abundance provides extremely fertile grounds for applied statistics. On one hand, the IT age applied statistics research is challenged by the massiveness of data which makes the fastest computer seem slow and data visulization difficult. On other hand, applied statistics research is also given an unprecedented opportunity to impact old and new fields outside statistics. Our faculty's applied statistics research spans a wide range of such fields including astronomy, geophyscs, remote sensing, AIDS research, genetics and bioinformatics, neuroscience, transportation, computer science, information and data compression, the census, demography and law, the theory of options pricing, and financial statistics.
Specifically, our interdisciplinary research can be grouped into four categories:

Physical Science:
Animal movement study (David Brillinger) *
Astrophysics (Philip Stark)
Astronomy (John Rice)
Bioinformatics/computational biology (Peter Bickel, Haiyan Huang, Michael Jordan, Nicholas P. Jewell, Juliet P. Schaffer, Terry Speed,
Environment risk analysis (David Brillinger, Mark van der Laan)
Neuroscience (David Brillinger*, Bin Yu)
Genetics (Steven Evans, Terry Speed)
Geophysics (Philip Stark)
Phylogenetic trees (Steve Evans, Elchanan Mossel)*
Seismology (David Brillinger)*

Social Science:
Census (David Freedman)
Educational technology (Philip Stark, Deborah Nolan)
Educational Statistics (Juliet P. Shaffer),
Federal Statistical System (Kenneth Wachter)
Law and statistics (David Freedman, Philip Stark)
Teaching of statistics (Deborah Nolan)

Engineering:
Artificial intelligence (Michael Jordan)
Computer vision (Peter Bickel)
Program debugging (Michael Jordan)*
Network tomography (Bin Yu)
Remote sensing (Bin Yu)
Signal/image processing (Martin Wainwright, Bin Yu)
Text Mining (Michael Jordan)*
Transportation modeling (Peter Bickel) and applications of functional data analysis and time series analysis to (John Rice)

Other areas:
Epidemiology (particularly of infectious diseases, including AIDS and SARS) (Nicholas P. Jewell)
Finance (Steven Evans, Noureddine El Karoui*)
Medical research (Mark van der Laan)

 

 

Probability

Research in probability ranges broadly from modern discrete probability and the theory of algorithms to classical and modern stochastic process theory.

Continuous Stochastic Processes
Jim Pitman has longstanding interests in distributional properties of multi-dimensional Brownian motion, and Yuval Peres has worked on the fine structure of sample paths of Brownian motion. Steve Evans has worked extensively on superprocesses and other measure-valued processes that arise in population biology.

Probability in Algorithms and Phylogeny
Mixing times for finite Markov chains are of interest both in the theory of algorithms and statistical physics, and in Berkeley are studied by David Aldous, Elchanan Mossel, Yuval Peres, and Alistair Sinclair. Phase transitions in hard combinatorial optimisations problems over random data are studied by Yuval Peres and David Aldous. Rigorous study of the much used but ill understood survey propogation algorithm is underway by Elchanan Mossel and Martin Wainwright. Elchanan Mossel also studies information theoretic limits to phylogenetic reconstruction. Steve Evans and Terry Speed have worked on the phylogenetic invariants in tree reconstruction and Steve Evans has also worked on phylogenetic methods in historical linguistics.

Infinite Discrete Random Structures
Yuval Peres works on a range of topics exemplified by percolation on non-amenable groups, and uniform and minimal spanning forests on groups and lattices.

Probabilistic Combinatorics
David Aldous and Jim Pitman have worked on size-asymptotics for random combinatorial structures such as trees, graphs, permutations and partitions, as well as irreversible models for coalescence and fragmentation. Probabilistic methodology leads to consideration of continuous limit objects ranging from interval splitting to the continuum random tree.