Title:
A Stochastic Model for Solitons
Speaker: Dr. Hosam M. Mahmoud
Department of Statistics, George Washington University
Date: January 23, 2004
Location: Funger Hall 221(Note: room change)
Time: 11:00-12:00 noon.
Abstract :
The soliton physics for the propagation of waves is represented by a
stochastic model in which the particles of the wave can jump ahead according
to some probability distribution. We demonstrate the presence of a steady
state (stationary distribution) for the wavelength. It is shown that the
stationary distribution is a convolution of geometric random variables.
Approximations to the stationary distribution are investigated for a large
number of particles. The model is rich and includes Gaussian
cases as limit distribution for the wavelength (when suitably normalized). A
sufficient Lindeberg-like condition identifies a class of solitons with normal
behavior. Our general model includes, among many other reasonable
alternatives, an exponential aging soliton, of which the uniform soliton is
one special subcase (with Gumbel's stationary distribution). With the proper
interpretation, our model also includes the deterministic model proposed in
Takahashi and Satsuma (1990).
------------------------------------------------------------------------------------------------------------------------ Title: Flexible class of imputation models for incomplete multivariate
multilevel models
Speaker:
Dr. Recai M. Yucel
Institute for Health Policy,
Harvard Medical School
Date: January 26, 2004
Location: Funger Hall 321
Time: 4:00-5:00 p.m.
Abstract:
Many statistical analyses involving multilevel data are non-trivial
because of uncontrollable missing data. When missing data exist only
for the response variable, standard procedures (e.g. as implemented
in HLM or PROC MIXED) can be employed as they allow for imbalance or
missing data. These procedures, however, do not accommodate for truly
multivariate responses and/or missing covariates, and operate under
standard assumptions of linear mixed-effects models. In this paper, I will
present a variety of models and computational tools for creating multiple
imputations of missing covariates and responses in multilevel data
applications. These models rely on multivariate extensions of the
linear mixed-effects models and are flexible enough to accommodate a
variety of applications, e.g. multivariate clustered, longitudinal, or
longitudinal clustered data. The imputation procedures are based on Markov
Chain Monte Carlo simulation techniques. These techniques are illustrated with
two applications: growth curve modeling of adolescent alcohol use in a large
school-based longitudinal prevention trial and a crime victimization survey.
------------------------------------------------------------------------------------------------------------------------
Title: Limit Distributions in Diagonal Polya
processes
Speaker: Dr. Srinivasan Balaji
Department of Statistics, George Washington
University
Date: February 6, 2004
Location: Funger Hall 321
Time: 4:00-5:00 p.m.
Abstract:
We investigate the Polya process, which underlies the
growth of an urn of white and blue balls growing in real
time. A partial differential equation governs the
evolution of the process. For urns with (forward or
backward) diagonal ball addition matrix the partial
differential equation is amenable to asymptotic
solution. In the case of forward diagonal matrix we find
a solution via the method of characteristics; the
numbers of white and blue balls, when scaled
appropriately, converge in distribution to independent
Gamma random variables. The method of characteristics
becomes a bit too involved for the backward diagonal
process, except in degenerate cases, where we have
Poisson behavior. In nondegenerate cases, constant
limits are found via the method of moments, and matrix
formulation involving a Leonard pair.
------------------------------------------------------------------------------------------------------------------------
Title: Profile Likelihood Inferences on
Semiparametric Varying-Coefficient Partially Linear
Models
Speaker: Tao Huang (University of North Carolina)
Date: February 17, 2004
Location: Funger Hall 322
Time: 4:00-5:00 p.m.
Abstract:
Varying-coefficient partially linear models have
received much attention in recent years and been applied
to many disciplines, including biomedical sciences,
economics, sociology and engineering sciences. Yet,
their estimation and inferences have not been
systematically studied. This talk proposes a profile
least-squares technique for estimating parametric
components. The asymptotic normality of the profile
least-squares estimator is studied. The main focus is
the examination of whether the generalized likelihood
techniques that were developed by Fan, Zhang and Zhang
(2001) are applicable to the testing problems in the
parametric component fsemiparametric models. Profile
likelihood ratio tests are introduced. We demonstrate
that the profile likelihood ratio statistics are
asymptotically distribution-free and follow
÷2-distributions under null hypotheses. This not only
unveils a new Wilks type of phenomenon, but also
provides a simple and useful method for semiparametric
inferences. In addition, Wald type of statistics in the
semiparametric models are introduced, and are
demonstrated to possess a similar sampling property to
profile likelihood ratio statistics. A new and simple
bandwidth selection technique is proposed for
semiparametric inferences in the partially linear
models. Both simulated and real data are presented to
illustrate the methodology.
------------------------------------------------------------------------------------------------------------------------
Title: NCI’s Biostatistics Grant
Portfolio and NIH Funding Mechanism
Speaker: Dr. Ram Tiwari (NIH/NCI)
Date: February 20, 2004
Location: Funger Hall 321
Time: 4:00-5:00 p.m.
Abstract:
The talk consists of two parts. In Part I, I will
talk about our newly released website: www.statfund.cancer.gov
, which contains information about a large proportion of
NIH’s funded grants in Biostatistics. These grants are
housed in the Division of Cancer Control and Population
Sciences at the National Cancer Institute (NCI). I will
also discuss various funding opportunities in (Bio)statistics
at NCI. In Part II, I will go over NIH’s funding
mechanisms and discuss the grant review process at NIH
in great detail.
-----------------------------------------------------------------------------------------------------------------------
Title: Statistical methods for identifying differential gene-gene interaction patterns
Speaker: Dr. Yinglei Lai
Center for Statistical Genomics and Proteomics
Department of Epidemiology and Public Health
Yale University School of Medicine
Date: February 24, 2004
Location: Funger Hall 322
Time: 4:00-5:00 p.m.
Abstract:
To understand cancer mechanisms, it is important to
explore molecular changes in cellular processes from
normal state to cancerous state. In this talk, we
address statistical methods for identifying differential
gene-gene interaction patterns in different cell states.
For efficient pattern recognition, we extend the
traditional F-statistic and obtain an Expected
Conditional F-statistic, which systematically integrates
statistical information about differences of locations
and correlations. We also propose a statistical method
for data transformation to eliminate outlier problem.
Our approach is applied to a microarray gene expression
data set for prostate cancer study. For a gene of
interest, our method can select other genes that have
differential gene-gene interaction patterns with this
gene in different cell states. Among 10 most frequently
selected genes, there are genes hepsin, GSTP1 and AMACR.
These 3 genes were recently proposed to be associated
with prostate cancer. But, it is difficult to identify
genes GSTP1 and AMACR by finding differentially
expressed genes. Using tumor suppressor genes PTEN, RB1
and TP53, we identify 7 genes that also include hepsin,
GSTP1 and AMACR. We show that genes associated with
cancer may have differential gene-gene interaction
patterns in different cell states. Our statistical
approach is capable of discovering such patterns.
-----------------------------------------------------------------------------------------------------------------------
Title: Statistical methods for identifying differential gene-gene interaction patterns
Speaker: Dr. Xueli Liu
University of California at Los Angeles
Date: February 26, 2004
Location: Funger Hall 321
Time: 4:00-5:00 p.m.
Abstract:
This talk is comprised of two parts.
In the first part, I will talk about my Ph.D. thesis
work. We propose a functional convex synchronization
model, under the premise that each observed curve is the
realization of a stochastic process. Monotonicity
constraints on time evolution provide the motivation for
a functional convex calculus with the goal of obtaining
sample statistics such as a functional mean. We derive a
functional limit theorem and asymptotic confidence
intervals for functional convex means. This
nonparametric time-synchronized algorithm is also
combined with an iterative mean updating technique to
find an overall representation that corresponds to a
mode of a sample of gene expression profiles, viewed as
a random sample in function space.
In the second part, I will talk about novel
statistical methods for the analysis of tissue
microarray data. Tissue microarrays (TMAs) represent a
high throughput tool for studying protein expression
patterns in tissue specimens. In performing TMA
analysis, the tissue is immunohistochemically stained
and scored by a pathologist based on tumor marker
staining scores. It is standard practice to select a
single staining cutoff that stratifies the population
based on an endpoint of interest. However, if the
dichotomized staining score is included in a Cox model
that uses the same outcome that was used to dichotomize
the staining data, the significance of the biomarkers
may be overstated. We introduce a new method (random
forest pre-validation) that circumvents this bias
problem. The idea is to summarize all staining scores
into a single scalar M which can be used as covariate in
a Cox regression model. We demonstrate the use of this
method to assess the prognostic significance of eight
biomarkers for predicting survival in patients with
renal cell carcinoma. Our proposed method avoids
problems associated with multi-collinearity and
over-fitting. We also carry out a cross-validation
scheme to compare the predictive power of different
prognostic models.
-----------------------------------------------------------------------------------------------------------------------
Title: Model Selection in Irregular Problems:
Applications to Mapping QTLs
Speaker: Professor David Siegmund
Department of Statistics, Stanford
University
Date: March 26, 2004
Location: Funger Hall, 221
Time: 11:00-12:00 p.m.
Abstract:
Two methods of model selection are discussed for
change-point like problems, especially those arising in
genetic linkage analysis. The first is a method that
selects the model with the smallest p-value, while the
second is a modification of the Bayes Information
Criterion (BIC). The methods are compared theoretically
and on examples from the literature. For these examples,
they are roughly comparable although the p-value based
method is somewhat more liberal in selecting a high
dimensional model.
-----------------------------------------------------------------------------------------------------------------------
Title: Distances in Random Tries via Analytic
Probability: the Oscillatory Distribution
Speaker: Costas Christophi
Department of Statistics, GWU
Date: March 29, 2004
Location: Funger Hall, 321
Time: 11:00-12:00 p.m.
Abstract:
We investigate Dn, the distance between randomly
selected pairs of nodes among n keys in a random trie,
which is a kind of digital tree. Analytic techniques,
such as the Mellin transform and an excursion between
poissonization and depoissonization, capture small
fluctuations in the mean and the variance of these
random distances. The mean increases logarithmically in
the number of keys, but curiously enough the variance
remains O(1), as n grows to infinity. It is demonstrated
that the centered random variable Dn* = Dn –
Floor(2log2n) does not have a limit distribution, but
rather oscillates between two distributions.
-----------------------------------------------------------------------------------------------------------------------
Title: Solution to a Fuctional Equation and its
Application to Stable and Stable- Type Distributions
Speaker: Professor : G. G. Hamedani
Department of Mathematics, Statistics and Computer Science
Marquette University
Date: April 16, 2004
Location: Funger Hall, 321
Time: 4:00-5:00 pm
Abstract:
The main purpose of this talk is to completely
characterize all continous complex-valued functions
phi(t) with domains R+ or R satisfying phi(t)=(phi(a1t))^gamma1=(phi(a2t))^gamma2,
where a1~=1, a2~=1, gamma1, gamma2 are positive numbers
with irrational log a1/log a2. Then we mention the
application of the solution of the above equation to
certain distributions.
-----------------------------------------------------------------------------------------------------------------------
Title: A Three-Way, Three-Mode Hybrid Factor/Components Analysis Model
Speaker: Anil Chaturvedi
Capital One Services
Date: April 30, 2004
Location: Funger Hall, 321
Time: 4:00-5:00 pm
Abstract:
This paper presents an approach to enhancing the traditional multivariate factor/components analyses models for three-way (e.g., Brands x
Product Attributes x Market Segments), three-mode interval-scaled data. It enables the extraction of a combination of continuous (a la the
CANDECOMP/PARAFAC model of Carroll and Chang, 1970 and Harshman and Lundy, 1984) as well as discrete factor scores and
factor loadings for three-way, three-mode data, thus enabling a richer exploration of the data-set at hand. It precludes the assumption that
there is only continuous factor/component structure in such data. Users can use the suggested approach to try to examine the presence of
hybrid structure present in the data - be it discrete or continuous. This model is also a special case of a very general class of models and
methods called CANDCLUS presented by Carroll and Chaturvedi (1994). We present various results from this three-way, three-mode
factor/components analysis model applied to data gathered from a marketing research study.
The series hosts a seminar about twice a month on current
research topics. The seminar often features an invited
guest speaker and occasionally local faculty members,
students or others affiliated with the department. The
usual time of the seminar is 11:00 a.m. on Fridays. Professor
Reza
Modarres (E-mail : reza@gwu.edu)
is the Seminar Series Coordinator.
--------------------------------------------------------------------------------
The contact person is Reza Modarres at Reza@gwu.edu or 202-994-6359.
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