Information Concerning the STA 6934 Offerings
Monte Carlo Statistical Methods
Monte Carlo methods are increasingly used in many scientific areas,
including statistical physics (where they originated), Bayesian and
frequentist statistical inference, and image reconstruction. The
basic idea is to carry out a simulation to estimate quantities of
interest that cannot be computed analytically. This course will
discuss a number of standard Monte Carlo schemes, and then Monte Carlo
methods based on Markov chains.
Prerequisites: STA 6326-7
Statistical Analysis of Gene Expression Microarray Data
This course is designed to give an introduction to gene microarray
technology and discuss various statistical methods that can be used
for analyzing such high-throughput data. Topics covered include both
low level and high level analysis. Conceptual and methodological
underpinning of data analysis tools will be described. Implementation
of analysis approaches using R package will be discussed in several
lab sessions. The goal is to provide guidance in deciding which
statistical approaches and packages may be used for particular
projects and correctly interpreting the results. Potential research
topic will also be discussed in the course. Performance in the course
will be evaluated based on computing assignments, in-class
presentation and a final data project.
Prerequisites: STA 4321-2; knowledge of STA 5701 and programming
experience in R/Splus or matlab will be very helpful.
Topics in Basic Analysis
An introduction to real analysis, including set theory, the real
numbers with heavy emphasis on the completeness property, sequences of
real numbers and convergence concepts, limit superior and limit
inferior of sequences, metric space topology, compactness, the
Bolzano-Weierstrass theorem and the Heine-Borel Theorem, continuity of
functions, sequences of functions, infinite series, Riemann
integration. Emphasis is placed on rigorous development of
mathematical concepts and the development of critical thinking
skills. The course is designed to prepare students for the study of
measure-theoretic probability (STA 6466-7).
Prerequisites: As a minimum the student should have complete three
semesters of honest calculus. Additional work in mathematics would be
helpful but strictly speaking not necessary.
Note: It is not appropriate to think of this course as "Calculus Four"
or "Advanced Calculus". Indeed, it would be better to think of it as
"Calculus Zero" or "Calculus Infinity". We will be concerned with
foundational matters. For example, instead of developing (say) a dozen
or so tests for convergence of series, we will present just a few and
emphasize what it really means for a series to converge.
Advanced Topics in Linear Models
The course is a continuation of STA 6246 (Linear Models). It mainly
deals with the analysis of unbalanced mixed models. In particular, it
covers the following topics: Estimation of variance components for
unbalanced models, measures of data imbalance, exact tests concerning
unbalanced random and mixed two-way models, exact tests concerning
unbalanced random models with unequal cell frequencies in the last
stage, comparison of designs for random models, and an introduction to
generalized linear mixed models.
Prerequisites: STA 6246
Topics in Stochastic Processes
Basic theory of Markov chains.
Prerequisites: STA 6466-7
Spatial Statistics
Prerequisites:
Markov chain Monte Carlo
Prerequisites:
Bayesian Methods
Prerequisites:
Longitudinal Data
Likelihood-based and semiparametric methods for longitudinal data.
Also, discussion of how to deal with missing data and its impact both
theoretically and practically on inference.
Prerequisites: STA 6326-6327 and STA 6207-6208 and Stat 6246.
Inference and Modeling for Research
This course is designed for students who have completed one or more
introductory-level courses in statistics and require additional
training in model-based inference and methods of data analysis. This
training will include (1) an overview of theoretical results needed
for computing likelihood-based inferences from either a frequentist
(classical) or Bayesian perspective, and (2) development of
computational skills needed to use these results in the analysis of
data. An integral part of the course is the formulation of statistical
models to meet scientific objectives.
Prerequisites: Students must have completed at least one
introductory-level course in statistics (equivalent to STA 6166) and
one course in calculus (equivalent to MAC 2233). Previous knowledge of
a computer programming language is not required; however, the S
programming language (on which R is based) will be used extensively.
Bayesian Theory
Prerequisites: