| Eric V. Slud Professor, Statistics Program Department of Mathematics University of Maryland College Park, MD 20742 |
|
Research
Interests Info on Older RIT's Links |
Past Teaching: Mini-Courses
Mini-Course on Cross-Classified Factor
Analysis
Lecture
(10/17/05) Mathematical Challenges in Cross-Classified
Factor Analysis
Summary of interesting mathematical issues
related to PhD theses about Factor Analysis
by my former students
Yang Cheng(2004) and Sophie (Hsiao-Hui) Tsou (2005).
Mini-Course on Markov Chain Monte Carlo
(Statistical Simulation Techniques)
Spring '04: 4/21, 4/28
Slides can be found at links indicated under each
lecture below.
The lecture topics are as follows:
Lecture
1 (4/21/04) Metropolis Hastings Algorithm --
Motivation from Accept-Reject
simulation methodology and from Markov
Chain theory. Extended example and issues
involved in the choice of `proposal
Markov chain' from which the Metropolis-Hastings
chain is built. Gibbs Sampler motivation.
Lecture
2 (4/28) Recap of Gibbs Sampler
motivation. Testing for Markov Chain Monte Carlo
convergence from the internal evidence
of the Gibbs Sampler trajectory. Statistical examples:
Bayesian statistical computation and
frequentist treatment of hierarchical statistical models.
Mini-Course on Statistics of Survival Data
(Fall '02: 11/6, 11/13, 11/20)
Slides can be found at links indicated under each
lecture below.
The lecture topics are as follows:
Lecture 1
(11/6/02) Survival Times, Death Hazards & Competing Risks
Lecture 2
(11/13) Population Cohorts and Martingales
Lecture 3
(11/20) Survival-data likelihoods with Infinite-Dimensional
Parameters
(1) Fall '05 RIT on
Statistics of Models with Growing Parameter Dimension
(2) Spring '04 RIT on Meta-Analysis. Click
here
for web-page.
Briefly,
meta-analysis concerns the simultaneous statistical analysis
of a number of
related studies or datasets within a single statistical model. The fact
that parameters are
shared across datasets (e.g. a treatment-effectiveness parameter assumed
constant
across a number of separately conducted clinical studies of
the effectiveness of the same
treatment regimen for the same disease) allows the possiblity of increasing
sensitivity or
power of statistical tests. However, such an increase in precision comes
at the price of
simultaneous model assumptions whose compatibility with the data must be
validated.
This RIT was an outgrowth of the Fall '03 RIT on Large Cross-Classified
Datasets
(see web-page linked below for details).
(3) Spring and Fall '03 RIT on Statistics of Large
Cross-Classified Datasets:
see
RITF03
web-page .
(4) Intensive Seminar, Fall 2002. See
plan
for details.
In Fall 2002, I ran a
`research interaction' seminar including my own
graduate advisees
and others, on the mathematical & statistical
topics which more broadly correspond to
the overlap
of my students' thesis projects and most of my own current
research interests,
namely Statistics of Large Cross-Classified Datasets.
Roughly speaking, these are
problems in which
there is a large sample-size n, but where the predictor variables
and/or
cross-classifications of the sample units become more complicated or
numerous
as n gets large. Such problems range from Semiparametric
Statistical Inference to
Order-selection problems
in regression and time series, to Classification
and Clustering
as in the Microarray
data problems mentioned below. These problems suggest the
need for a new
Asymptotics which explicitly recognizes the growth of the parameter-
space of a probability
model as a function of the size n of the dataset.
(5) Intensive Seminar, Spring 2002.
See
plan
for details.
In Spring 2002,
following up on the Fall 2001 seminar described below, I ran an intensive
seminar on
statistical analysis of DNA Microrarrays, for students considering
research
in this
area. Data-analysis figured prominently, performed by me and
also by two of the
several graduate students who participated.
(6) Genomics/Microarray
Seminar Fall 2001, AMSC 699:
Mathematical Topics in
Functional Genomics. Click
here
for the reading list.
Other Past Teaching
(1)
Spring '04, introductory course Stat 470
on Actuarial Mathematics, taught primarily
from book
notes which I wrote. Coverage includes theory of interest, life tables,
review of
probability
theory, expectations of time-discounted insurance costs and premiums
calculated
from life tables, and special models of mortality.
See
the course web-page
(from which the main
text can be downloaded a chapter at a time) for further
details.
(2)
Spring '04 Stat 798C,
Computational Methods in Statistics, a graduate
introduction
to statistical computing
with emphasis on the Splus (or R) and SAS computer packages.
(I also taught this
course in Spring '03.)
(3) Fall '03, Stat 798S, topics course on Survival Analysis .
(4)
Spring '03, Stat 770 ,
a course on Analysis of Categorical Data, taught out
of the book, Categorical Data Analysis, by A. Agresti.
(I) Survival data analysis, which includes both semiparametric
inference and clinical
trial design issues. The semiparametric work emphasizes
maximization of variants
of nonparametric likelihoods, especially in
Transformation and Frailty models.
Further
work on a general approach to efficient semiparametric estimation described
in
slides
from a talk given in the IISA Conference, June 14, 2002. Other current
work
relates
to decision-theoretic
optimal
early-stopping procedures in clinical trials.
For slides of a Stat Seminar I gave in Fall '03 at NIH on asymptotic
theory of Semiparametric
statistical procedures in Transformation models, click
here .
(II) Census
statistics, specifically demographic modelling of nonresponse to
national
surveys, with particular application to
Weighting
Adjustment and Small Area
Estimation (SAE). Much of my small-area estimation work has
been directed
toward the SAIPE
(Small Area Income
and Poverty Estimation ) program of
the Census Bureau. See for
example the
comparative SAE study.
My
methodological research in this area
includes small-area and MSE estimation
from survey data satisfying nonlinearly
transformed Fay-Herriot models or
left-censored
Fay-Herriot models.
Some
recent work on internal evaluation of biases due to weighting
adjustment for
nonresponse in a longitudinal survey (SIPP, Survey on Income and Program
Participation) is described in
my Nov. 2007 FCSM talk. A paper
describing the
contents of that talk more fully can be found
here.
(III) Large-scale data problems with emphasis on cross-classified data,
Principal
Components (paper on representation of tongue surface during
speech,
recently appeared in the journal Phonetica), and
clustering. More recently,
I have had two students (Yang Cheng and Sophie Tsou) obtain PhD's working
on Factor Analysis models. Papers extending that work are now in preparation
and will be posted to this space shortly. A talk I gave on this work
in 2005
[and then again in the Diffusion Wavelet RIT in Fall 2007] can
be found here.
(IV) Stochastic processes, currently emphasizing high-dimensional
Markov
processes applied to
equilibria
in Economics (paper in Journal of Economic
Theory, for which 2nd pdf file in directory contains Figure); to Protein-folding;
and to ascertainment of number of distinct DNA `species' from sequencing
experiments.