Title: Semiparametric Bayesian Techniques for Problems
in Circular Data
Speaker: Professor Kaushik Ghosh
Department of Statistics, The George Washington University
Date: January 25, 2002
Location: Funger Hall 321
Time: 11:00 a.m.
------------------------------------------------------------
Many scientific experiments generate observations that
are two-dimensional directions or are periodic with
a known period. Such data can be represented by points
on a circle --- hence the name circular data. In this
work, we consider the problems of prediction and tests
of hypotheses for circular data in a semiparametric
Bayesian setup. Observations are assumed to be independently
drawn from the von Mises distribution and uncertainty
in the location parameter is modeled by a Dirichlet
Process Prior. For the prediction problem, we present
a method to obtain the predictive density of a future
observation, and, for the testing problem, we present
a method to obtain the posterior probabilities of the
hypotheses under consideration. Incorporation of the
semiparametric model gives us more flexibility and robustness
against prior mis-specifications. While analytical expressions
are intractable, the methods are easily implemented
using the Gibbs sampler. We illustrate their use with
examples from Medicine and Geology.
----------------------------------------------------------
Title: A Transaction Price Index for Air Travel
Speaker: Dr. Janice Lent
U. S. Bureau of Labor Statistics
Joint work with Alan Dorfman, U. S. Bureau of Labor
Statistics
Date: 11:00-12:00 pm, February 8, 2002
Location: Funger Hall 308
Time: 11:00 a.m.
------------------------------------------------------------
We present research undertaken to develop a price index
estimator based on data from the U.S. Transportation
Department's (DOT's) Origin and Destination (O&D)
Survey. Through this survey, the DOT collects prices
actually paid by consumers for air travel; these may
differ considerably from "list prices" (used
in the official U.S. airfare CPI) due to the airlines'
use of complex pricing structures. Since the O&D
survey was not designed to provide data for price index
estimation, however, the research involves testing unique
imputation and across-time matching procedures. After
a brief introduction to the general field of price index
estimation, we describe our methodology and compare
our experimental index series to the official airfare
CPI series.
----------------------------------------------------------
Title: Maximum Likelihood Estimation for Fractional
Diffusions
Speaker: Dr. Jay Bishwal
Department of Mathematics
University of Cincinnati
Date: March 1, 2002
Location: Funger Hall 307
Time: 2:00-3:00 p.m.
------------------------------------------------------------
Recently, it has been empirically found that log share
prices allow long range dependence between returns on
different days. In view of this, it becomes necessary
to extend the diffusion models to processes having long
range dependence. One way is to model these data by
stochastic differential equations with fractional Brownian
motion (fBM) driving term, with Hurst index greater
than 1/2. The fbm being not a Markov process and not
a semi-martingale, except where the Hurst index equals
1/2, the classic Ito calculus cannot be used to develop
the theory. First, recent developments in fractional
stochastic calculus: stochastic integral with respect
to fBM, fractional Ito formula and fractional Girsanov
formula will be reviewed. The use of Volterra and Dirichlet
stochastic calculus will be emphasized. The long time
asymptotic behaviour of the maximum likelihood estimator
in the drift parameter in the nonlinear SDE driven by
fBM will be studied. Some further problems on estimation
in fractional diffusions based on discrete observations
will be discussed.
---------------------------------------------------------------
Title: Probabilistic Analysis of Algorithms by the
Contraction Method.
Speaker: Professor Ralph Neininger
Department of Computer Science
McGill University, Montreal
Date: 11:00-12:00 pm, March 15, 2002
Location: Funger Hall 308
Time: 11:00 a.m.
------------------------------------------------------------
The contraction method provides a framework to prove
limit laws for sequences of random variables satisfying
recurrence relations on the level of distributions as
they arise for parameters of recursive algorithms or
random tree structures. The name of the method refers
to the characterization of the occurring limit distributions
as fixed-points of maps between spaces of probability
measures, which turn out to be contractions with respect
to appropriate probability metrics. In this talk an
overview of this method is given with particular emphasis
on recent developments.
--------------------------------------------------------------
Title: OPTIMAL DESIGNS FOR PHASE I CLINICAL TRIALS
Speaker: Professor William F. Rosenberger
Department of Mathematics and Statistics
University of Maryland, Baltimore County
Date: 11:00-12:00 pm, April 5, 2002
Location: Funger Hall 308
Time: 11:00 a.m.
------------------------------------------------------------
A broad approach to the design of phase I clinical
trials for the efficient estimation of the maximum tolerated
dose is presented. The method is rooted in formal optimal
design theory and involves the construction of constrained
Bayesian c- and D-optimal designs. The imposed constraint
incorporates the optimal design points and their weights
and ensures that the probability that an administered
dose exceeds the maximum acceptable dose is low. Results
relating to these constrained designs for log doses
on the real line are described and the associated equivalence
theorem is given. The ideas are extended to more practical
situations and specifically to those involving discrete
dose spaces. In particular, a Bayesian optimal design
scheme comprising a pilot study on a small number of
patients followed by the allocation of patients to doses
one-at-a-time is developed and its properties explored
by simulation.
----------------------------------------------------------------
Title: Asymptotics of Brownian and Diffusion Sample
Paths
Speaker: Dr. Srinivasan Balaji
Department of Mathematical Sciences: New Jersey Institute
of Technology
Date: 11:00-12:00 pm, April 12, 2002
Location: Funger Hall 321
Time: 11:00 a.m.
------------------------------------------------------------
The study of stability properties like recurrence,
transience, and positive recurrence of stochastic processes
are of great importance in varied applications including
heavy traffic queuing networks, structural stability,
and stochastic finance. In this talk we will focus our
attention mainly on diffusion processes. Initially some
elementary properties of Brownian motion, the basic
diffusion process, will be discussed in detail. Conditions
for stability of diffusions and reflecting diffusions
will be obtained. Also the finiteness or infiniteness
of passage time moments for multidimensional diffusions
will be considered. Finally some interesting open problems
and future directions will be discussed.
---------------------------------------------------------------
Title: Baseline Adjustment by Inducing a Partial Ordering
When Measurements are Ordered Categories
Speaker: Dr. YanYan Zhou
Department of Mathematics and Statistics, University
of Maryland, Baltimore County
Date: 3:30-4:30 pm, April 16, 2002
Location: Funger Hall 321
Time: 11:00 a.m.
------------------------------------------------------------
The purpose of baseline correction in between-patient
studies is to ensure that the two treatments groups
are not statistically different at the beginning of
the study. However, adjusting for baseline values is
not an easy task and there is no unique way of doing
it. One method is to fit a cumulative logistics regression
model. But this comes with the common burden of parametric
assumptions, which may not have any relevance to the
data generating process. The other popular option is
to resort to nonparametric techniques such as the Mann-Whitney-Wilcoxon
test or Smirnov like tests. Each of these procedures
invokes an artificial order in the ordinal data. This
is a major drawback of such procedures yielding false
significance between categories which otherwise are
not comparable. In this talk, we seek to overcome the
aforementioned drawbacks of nonparametric baseline adjustment
procedures. We propose a new method, which adjusts for
baseline without relying on any specific assumptions
on the data generating process. The conditional exact
power of Smirnov-like tests are calculated under different
alternative hypotheses in order to compare them among
themselves as well as to the traditional tests.
---------------------------------------------------------------
Title: The Information Content of Trades: A Class of
Market Microstructure Models
Speaker: Dr. Anna Valeva
Department of Statistics and Applied Probability, University
of California, Santa Barbara
Date: April 18, 2002
Location: Funger Hall 321
Time: 10:00 a.m.
------------------------------------------------------------
Market microstructure is a relatively new field in
Economics. It deals with the study of the process and
outcomes of exchanging assets under explicit trading
rules. We focus on a class of models in which the market
specialist exploits the information content of trades
in order to set the bid-ask spread for a given asset.
The presence of asymmetric information is assumed, i.e.,
there are informed traders against which the market
specialist loses on average, but he/she is able to offset
the loss by trading against `noise' traders. Thus, asymmetric
information alone explains the existence of a bid-ask
spread, and provides insights into the adjustment process
of prices. While the idea for such type of models dates
back to the mid eighties, we introduce a dynamic way
of quantifying the information which informed traders
use. We discuss how volume of trade conveys information
about the true asset value to the market specialist.
The model also explains some empirical facts described
in the literature, namely, serial correlation in trades
and serial correlation in squared price changes.
---------------------------------------------------------------
Title: NONPARAMETRIC ESTIMATION OF CONDITIONAL SPATIAL
MEDIAN
Speaker: Dr. Ali Gannoun
University Montpellier II, Laboratoire de Probabilites
et Statistique
Montpellier, France
Date: 11:00-12:00 pm, April 19, 2002
Location: Funger Hall 308
Time: 11:00 a.m.
------------------------------------------------------------
In this talk, we generalize the notion of the univariate
conditional median to the multivariate case, and we
define the so-called L1-conditional median or spatial
conditional median. Then we propose a nonparametric
estimator of this median. As an application, we construct
multivariate and joint-horizon nonparametric predictors
for time series processes.
--------------------------------------------------------------------------------
The contact person is Reza Modarres at Reza@gwu.edu
or 202-994-6359.
|
