Our Faculty Research Interests
For a broader view, we asked each of our other faculty to describe
their interests briefly. To learn more, you'll have to phone,
e-mail, write or visit! We have included in this list emeriti
and some faculty in other departments who have courtesy
appointments in Statistics, as they all play an active role
with students and in research in the Statistics department.
Theodore W. Anderson
One of my areas of interest is multivariate statistical analysis,
which is the analysis of data consisting of multiple measurements on
each observational unit. Macroeconomic and psychometric data usually
have this nature. I have developed methodology for analyzing such
data. Many of the procedures involve reducing the dimensionality of
the important variability. A class of such methods arises in the
multivariate analysis of variance.
Another area of my interest is the analysis of time series, data
that accrue over time. Currently I am studying statistical inference
for spectral distributions of stationary statistical processes and
large-sample theory for autoregressive models.
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Amir Dembo
My Ph.D. in Digital Signal Processing (Electrical Engineering) was
followed by research on the analysis of Neural Networks. In time I
became more interested in probability theory and its
applications. This is what I am doing now, half-time in the statistics
department and half-time in the mathematics department.
A few examples are:
- Assessing which seemingly rare segments of DNA (or protein) may
be due to pure chance (jointly with Sam Karlin from the
mathematics department).
- Studying relationships between uncertainty inequalities in
information theory, statistics, mathematics and physics (jointly
with Tom Cover and Joy Thomas from this department and IBM,
respectively).
- With Ofer Zeitouni (Technion, Israel), writing a book on the
theory of large deviations and its applications.
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Jerome H. Friedman
I am interested in how to use the capabilities of modern day
computers to most effectively learn from data. These capabilities
include very rapid computation and sophisticated (dynamic) graphics
for scientific visualization. The goal is to develop computer based
tools that can extend our ability to analyze data beyond that provided
by the standard repertoire of statistical techniques that were
developed before the existence of readily available computing.
One such area that is receiving considerable recent attention is
machine learning ("neural networks"). Here one has a system
under study that responds to a set of simultaneous input signals. The
response is characterized by a set of output signals. The goal is to
learn the relationship between the inputs and the outputs in the most
general way possible. This exercise generally has two purposes:
prediction and understanding. With prediction one is given a set of
input values and wishes to predict or forecast likely values of the
corresponding outputs without having to actually run the
system. Sometimes prediction is the only purpose. Often, however, one
wishes to use the derived relationship to gain understanding of how
the system works. Such knowledge is often useful in its own right,
for example in science, or it may be used to help improve the
characteristics of the system, as in industrial or engineering
applications.
Another area that modern computing has made possible is data
exploration through graphic visualization. Here the goal is to
explore data to discover the unexpected. One attempts to use the
human gift for pattern recognition to detect un usual patterns in the
relationships among the measured quantities. This human gift is very
powerful at seeing (previously) undefined effects; one can be
surprised at seeing something that was not at all anticipated, leading
possibly to a new discovery. Unfortunately the human gift for pattern
recognition is limited to low (two to three) dimensions, whereas the
data often involve many more than three simultaneously observed
quantities. One must map this high dimensional data to lower
dimensional representations for visualization. The purpose of
research in this field is two-fold: first to discover mappings that
reduce the information content as little as possible, and second, to
make innovative use of computer graphics technology to in crease
humanly perceivable dimensionality to be as high as possible. The
first part involves research in statistical information theory, and
the second research in computer graphics and scientific data
visualization.
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Trevor Hastie
I am an applied statistician, with a joint position in Biostatistics
in the medical school. Most of my research is generated from
applications with which I am involved. I tend to teach applied classes
as well. For example I have taught parts of the 315,316 Ph.D first
year graduate series, as well as 341, an applied multivariate class,
and 315, our new Modern Applied Statistics class.
My research has focussed on function approximation and curve fitting
within a variety of different applications. A common theme in my
research so far has been to try and provide methodology that naturally
bridges the gap between the traditional well tested linear techniques,
and the newer more adventurous nonparametric frontiers.
Generalized additive models adapt nonparametric regression technology
to provide more flexibility to the usual linear models used in applied
areas, such as logistic and log-linear models. Principal curves and
surfaces generalize linear principal components by allowing nonlinear
coordinate functions. Currently I am interested in flexible methods
for classification, and my research is focussed on developing richer
classes of models for this task, as well as to understand better the
nature of the classification problem.
Sometimes even the linear techniques are too rich, such as when the
variables are sampled versions of a smooth function or image. The
exponential growth in computer processing speed and storage has
allowed us to routinely gather data where each observation is one or
more digitized image. This has lead to a new field currently known as
functional data analysis, and is filled with many interesting (open)
problems, because the traditional techniques no longer work.
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Iain M. Johnstone
Much of my research is concerned with optimality in estimation how
well can you estimate a parameter, function or feature with a limited
amount of noisy data? Tools from statistical decision theory (akin to
those of game theory) and probability limit theorems for large samples
play a role. Sometimes the questions are basically for fun: why is
optimality of an estimator for Poisson data the same as recurrence of
a birth-and-death process; what on earth does it have to do with
isoperimetric inequalities from partial differential equations?
Alternatively, the theory may be abstracted from general scientific
methodology what's so marvelous about maximum entropy, why are
wavelets so wonderful? Othertimes, there is a tough practical issue
what is the real error rate of a classification rule (the obvious
estimates can be very, very wrong), and how well could you know it?
This last connects to my work in the Medical School, where I am
involved in various projects in arteriography, urology, heart surgery
clinical trials, geographic medicine and medical imaging.
Talking to a doc about her problem (not yours!) can be a welcome rest
from theory and vice versa!
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Helena Chmura Kraemer
I am an applied statistician particularly interested in the
development of statistical methodology and application in the
interstice area between biological and behavioral areas in medical
research. In particular, my interests concern the assessment of
reliability of measures, particularly diagnoses, assessment of the
effects of problems in this area, development of research strategies,
designs and analytic strategies to cope with such problems. Recently
this interest has expanded to modification of signal detection methods
to integrate different statistical approaches to assessment of the
quality and cost-effectiveness of medical tests. Underlying all these
is a long-standing interest in correlational methods, and in the issue
of power in research.
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Tze Leung Lai
My present research areas include sequential experimentation,
adaptive inference and control, stochastic optimization, time series
analysis and forecasting, regression analysis of censored and
truncated failure time data, design and analysis of clinical trials,
probability theory, and stochastic dynamical systems. My
methodological research in these areas has been motivated by and is
closely related to my applied interests in engineering systems,
financial economics, and medicine. I am also currently involved in
several research projects in the Division of Medical Informatics, the
Cancer Hyperthermia Laboratory, and the Center for AIDS Research at
Stanford.
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Ingram Olkin
Recently I have focused on statistical methods for combining the
results of independent studies. There is now a huge body of studies
that deal with specific problems. For example, there are over 750
experiments on the effect of cloud seeding, some of which may use
different seeding agents, may seed in different months, and so on. In
the health sciences there are many studies concerned with the effects
of a particular drug or treatment. For example, is a combination of
estrogen and progesterone effective in reducing osteoporosis in women,
or is aspirin effective in diminishing heart attacks? In each case,
different studies may use different populations, concentrations, or
frequency may vary, etc. The statistical problem is to provide
procedures for combining the results of these studies. The set of
such procedures has been called meta-analysis, in contrast to primary
or secondary analyses. My work to date has culminated in a book
(joint with Larry V. Hedges) on "Statistical Methods for
Meta-analysis."
An area of current interest is how to model
dependencies. The theory of inde pendent measures is well-developed,
but except perhaps for the normal distribution, there are many ways
for modeling non-normal bivariate distributions. The mechanisms for
such modeling may arise from statistical concepts, physical
structures, characterizations, mixtures, etc. Thus, we might expect
different models for the joint failure distributions of the engines on
an airplane, than the failure distributions of organs in the body.
This area is fascinating in that it permits one to study various
physical phenomena.
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Richard Olshen
My research involves statistics and mathematics as they apply to
problems in medicine. Typically, the applications are computer
intensive. They nearly always involve sample reuse methods.
Binary tree-structured methods for classification, regression, and
survival analysis have been an area of special interest. These
techniques entail optimally choosing sequences of yes-no questions
concerning predictors. The goal is to predict the out come for a test
case for which predictors are known, but the outcome is not.
Applications have included assessing the prognostic significance of
dose intensity in diffuse large-cell lymphoma and predicting
tendencies of certain organic compounds to cause ulcers.
Similar tree-structured algorithms, in this instance for clustering
vectorial pixel intensities, are used for data compression in digital
radiography.
Some research has focused on panel studies, in which many subjects
are followed longitudinally. Applications have included the study of
free speed human walking on a level surface, and, more recently,
cholesterol.
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Art Owen
My main teaching interests center on Ph.D. level applied
statistics. This includes the first year applied sequence, which has
been recently updated and the consulting laboratory. Since course work
alone is not enough, I encourage students to get involved in projects.
My current research interests are computer experiments and
empirical likelihood.
Computer experimentation is a new field in which methods of
statistics (exploration, prediction, interval estimation, design) are
adapted to deterministic responses com puted by simulators. These may
be simulating fluid flow, integrated circuits or combus tion.
Statistical methods are especially useful when the input space has a
high dimension and the simulations take a long time to run. The
language of probability is helpful in these problems. It can be
injected by modeling the functions as realizations of random
processes. I'm developing methods based on some randomness in the
design.
Empirical likelihood is a distribution free mode of inference based
on a nonparametric likelihood ratio. Some parametric likelihoods are
chosen mostly for convenience, and methods based on them may not be
consistent when the model is wrong. Empirical likelihood inferences
are consistent under much weaker conditions. It has sampling
properties similar to those of the bootstrap, but uses continuous
optimization instead of discrete resampling.
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David Rogosa
My research is in the development and application of statistical
methods in the behavioral and social sciences. My major publications
have been in the areas of longitudinal research (e.g., measurement of
change), methods for the design and analysis of behavioral
observations, and causal inference from experimental and
nonexperimental studies.
Another part of my statistical activities is consulting with State
and Federal gov ernmental agencies. One recent example is the
development of the California Accountability Index, a composite
measure of the quality and progress of public schools, for the
California State Department of Education.
My teaching is a mixture of undergraduate and graduate courses: For
undergraduates, an introductory course in the Department, and for
graduate students, service courses for the Psychology Department and
the School of Education plus advanced courses in psychometrics and
applied statistics (e.g. longitudinal research, evaluation
methods).
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Joe Romano
Statistics is concerned with making sense or inferences about the
world based on limited information and uncertainties. In contrast,
mathematics is exact. The goal is to prove theorems based on a
well-defined set of assumptions. It is the juxtaposition of statistics
and mathematics that I find intriguing and challenging. Mathematical
statistics serves to precisely quantify and explain what can be
learned through "experimentation," in spite of having to
acknowledge our uncertainty in the process.
While my own research has been theoretically oriented, much of it
has been motivated by a desire to understand practical statistical
methodology to obtain techniques they may be applied safely in
practice. I have been particularly interested in advancing
"nonparametric" techniques that do not rely on the
statistician having to invoke unverifiable assumptions. In my work, I
have tried to explore the extent of applicability of bootstrap and
resampling methods, as well as understanding their limitations. My
recent interests have focused on extending resampling methods to
problems in time series analysis.
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Charles M. Stein
I work mainly on a method of using elementary probabilistic ideas
for the solution of problems which are usually attacked by other
methods. There are applications to combinatorics, statistics, and
traditional problems in probability theory.
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Paul Switzer
Statistics can play an important role in the analysis of
environmental monitoring data, detection of temporal and spatial
trends, modeling the effects of human ac tivity on environmental
quality and climate, the articulation of environmental standards, the
optimization of pollution mitigation and control strategies, and the
assessment of environmental impacts. Many branches of statistical
theory can be brought together to address these problems including
spatial analysis, time series, extreme value theory, design of
experiments, and nonlinear response modeling
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Guenther Walther
Over the last few years I have been working in various areas: Estimation
under shape restrictions, the interplay of statistical accuracy and
computational complexity, and solar physics, where joint research with
the Applied Physics Department led me into time series analysis
and bootstrap and subsampling problems. Currently I am working on
a problem in flow cytometry (a technique for sorting cells) jointly
with the Medical School. That problem involves nonparametric mixtures,
and turned out to be interesting, challenging, and also happens to
reveal a beautiful theoretical aspect.
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