Note: Courses listed are those that have been taught in recent years. For a complete list of classes offered by all departments and by semester, see Directory of Classes, Office of the Registrar
Names represent recent and anticipated instructors for the listed courses. Advanced courses are taught in alternate years depending on demand.
Cross-Listed Courses
Graduate Courses
Advanced Graduate Courses
Special Topics
Fall 2003 Schedule
Graduate
and Advanced Undergraduate
101-STATISTICAL
METHODS I Prerequisite, Stat 31 or equivalent. Some familiarity with matrix algebra recommended, but not required. This course presents regression analysis and related techniques, and is recommended for students throughout the natural and social sciences who are interested in applying regression analysis in their research and/or understanding the statistical concepts underlying the methodology. The topics include simple and multiple linear regression, matrix representation of the regression model, statistical inferences for regression model, diagnostics and remedies for multicollinearity, outlier and influential cases, polynomial regression and interaction regression models, model selection, weighted least square procedure for unequal error variances, and ANOVA model and test. Statistical software SAS will be used throughout the course to demonstrate how to apply the techniques on real data. The main purposes of this courses is to let students know how to use regression methods properly in data analysis and lay the foundation for more advanced studies in statistics. Fall and Spring. Fan, Marron, Zhu. (3).
102- STATISTICAL
METHODS II
Prerequisite,
Statistics 101. Topics selected from: design of experiments; sample
surveys; nonparametrics; time-series; multivariate analysis; contingency
tables; logistic regression; simulation. Use of statistical software
packages. Spring. Fan, Marron, Nobel, Smith. (3).
104- SAMPLE
SURVEY METHODOLOGY (Biostatistics 164)
Prerequisite,
Statistics 102 or equivalent. Principles and methods associated with
survey sampling, including simple random sampling, stratified sampling
and cluster sampling. Questionnaire design, problems of nonresponse,
sources of nonsampling errors.Design, execution, and analysis of an
actual survey. Spring. Kalsbeek. (3).
107- ACTUARIAL
MATHEMATICS II (Mathematics 162)
Prerequisites,
Mathematics 161, Statistics 126. The theory introduced in Actuarial
Mathematics I is expanded to encompass more complex models of financial
transactions and risks. Spring. Staff. (3).
126- INTRODUCTION
TO PROBABILITY (Mathematics 146)
Prerequisite,
Mathematics 33. Introduction to mathematical theory of probability covering
random variables, moments, binomial, Poisson, normal and related distributions,
generating functions, sums and sequences of random variables, and statistical
applications. Fall and spring. Kelly, Nobel. 3).
127- MATHEMATICAL
STATISTICS
Prerequisite,
Statistics 126 or equivalent. Functions of random samples and their
probability distributions; introductory theory of point and interval
estimation and of hypothesis testing; elementary decision theory. Fall
and spring. Carlstein, Fan, Marron, Simons. (3).
Graduate
154- MEASURE AND
INTEGRATION Prerequisite, advanced calculus. Lebesgue and abstract measure and integration, convergence theorems, differentiation. Radon-Nikodym theorem, product measures. Fubini theorems. Lp spaces. Fall. Leadbetter. (3).
155- PROBABILITY
(Mathematics 195)
Prerequisite,
Statistics 154 or permission of instructor. Foundations of probability.
Basic classical theorems. Modes of probabilistic convergence. Central
limit problem. Generating functions, characteristic functions. Conditional
probability and expectation. Spring. Kelly. (3)
164- STATISTICAL
THEORY I
Prerequisite,
two semesters of advanced calculus. Probability spaces; Random variables,
distributions, expectation; Conditioning; Generating functions; Limit
theorems: LLN, CLT, Slutzky, -method, big- in probability; Inequalities;
Distribution theory: normal, chi-squared, beta, gamma, Cauchy, other
multivariate distributions; Distribution theory for linear models. Fall.
Simons. (3)
165- STATISTICAL
THEORY II
Prerequisite,
Statistics 164 or equivalent. Point estimation; Hypothesis testing and
confidence sets; Contingency tables, nonparametric goodness-of-fit;
Linear model optimality theory: BLUE, MVU, MLE; Multivariate tests;
Introduction to decision theory and Bayesian inference. Ji, Marron,
Simons. Spring. (3)
174- APPLIED
STATISTICS I
Prerequisite,
permission of the instructor. Basics of linear models: matrix formulation,
least squares, tests; Computing environments: SAS, MATLAB, S+; Visualization:
histograms, scatterplots, smoothing, QQ plots; Transformations: log,
Box-Cox, etc.; Diagnostics and model selection. Fall. Smith. (3)
175- APPLIED
STATISTICS II
Prerequisite
Stat 174 or permission of the instructor. ANOVA (including nested and
crossed models, multiple comparisons); GLM basics: exponential families,
link functions, likelihood, quasi-likelihood, conditional likelihood;
Numerical analysis; numerical linear algebra, optimization; GLM diagnostics;
Simulation: transformation, rejection, Gibbs sampler. Spring. (3)
184- STOCHASTIC
PROCESSES
Prerequisites
for nonstatistics majors, Statistics 126 and permission of instructor.
Discrete Markov chains; Continuous Markov chains: Poisson, birth-death,
etc.; Stationary processes. Fall. Ji. (3).
185- TIME SERIES
AND MULTIVARIATE ANALYSIS
Prerequisite,
Statistics 126. Time Series: Exploratory and graphical analysis; Time
domain analysis and ARMA models; Fourier analysis: FFT, periodogram,
smoothing; State space analysis: Kalman filter, dynamic models. Multivariate:
Principal components, canonical correlation; Classification, clustering;
Dimension reduction: projection pursuit, alternating conditional sliced
inverse regression. Spring. Leadbetter, Simons. (3)
190- CONSULTING
Prerequisite,
permission of instructor. Projects are assigned by the instructor. Typically
these projects relate to requests for statistical consulting assistance
from outside the Department. The class meets once per week over an academic
year for a total of three credit hours. Fall, Spring. Marron, Smith.
194- DESIGN
AND ROBUSTNESS
Corequisite,
Statistics 165. Design: Classical designs (BIB, Latin square, fractional
factorial, industrial designs, Taguchi; Optimal designs: D-optimality,
etc.; Sequential designs: sequential probability ratio test, Stein 2-stage.
Robust methods: M-, L-, R-estimates, breakdown, influence curves; bootstrap,
jackknife, cross-validation. Fall. Marron (3)
195- BAYESIAN
STATISTICS AND GENERALIZED LINEAR MODELS
Corequisites,
Statistics 174 and Statistics 165, or permission of the instructor.
Bayes factors; Empirical Bayes, formulation, Stein effect; Classical:
EM, Laird-Ware; Hierarchical: prior, MCMC. GLM specific models: Binomial
regression, polytomous regression, Cox proportional hazard, log linear.
Spring. (3)
Cross-Listed
Courses in Other Departments
156- COMBINATORIAL
MATHEMATICS (Mathematics 148) Prerequisite, Mathematics 81 or equivalent, or permission of the instructor. Topics chosen from: generating functions, Polya's theory of counting, partial orderings and incidence algebras, principle of inclusion-exclusion, Moebius inversion, combinatorial problems in physics and other branches of science. Fall. Brylawski. (3).
158- INTRODUCTION
TO GRAPH THEORY (Mathematics 149)
Prerequisite,
Mathematics 116, 137, or 147. Basic concepts of directed and undirected
graphs, partitions and distances in graphs. Planar and nonplanar graphs.
Matrix representation of graphs, network flows, applications of graph
theory. Staff. (3).
160- APPLIED
MULTIVARIATE ANALYSIS I (Biostatistics 166)
Prerequisite,
Statistics 102. Application of multivariate techniques with emphasis
on the use of computer programs. Multivariate analysis of variance,
multivariate multiple regression, weighted least squares, principal
component analysis, canonical correlation, and related techniques. Spring.
Muller. (3).
171- INTRODUCTION
TO NONPARAMETRIC STATISTICS (Biostatistics 256)
Prerequisite,
Biostatistics 160 or equivalent. Theory and application of nonparametric
methods for various problems in statistical analysis. Includes procedures
based on randomization, ranks, and U-statistics. A knowledge of elementary
computer programming is assumed. Fall. Bangdiwala. (3).
181-DETERMINISTIC
MODELS IN OPERATIONS RESEARCH (Mathematics 151, Operations Research
181)
Prerequisite,
Mathematics 147. Linear, integer, nonlinear and dynamic programming,
classical optimization problems, network theory. Fall. Provan, Tolle.
(3).
Advanced
Graduate
210- DESIGN AND
ANALYSIS OF EXPERIMENTS Prerequisite, Statistics 194. The principles of the design and analysis of experiments. Latin and Graeco-Latin squares, incomplete block designs, factorial experiments. Confounding, fractional factorials, split plots, missing plots. Interblock analysis, covariance analysis. Response surfaces. (3).
211- SPECIAL
TOPICS IN THE DESIGN OF EXPERIMENTS
Prerequisite,
Statistics 150 or 194. Factorial experiments, construction and analysis
of symmetrical, mixed, and fractional factorial designs. Orthogonal
and balanced arrays. Response surface methodology. Mixture and screening
designs. Optimality of designs. Recent developments. (3).
212- COMBINATORIAL
PROBLEMS OF THE DESIGN OF EXPERIMENTS
Prerequisite,
Statistics 194. Finite groups, fields, and geometries. Difference sets.
Orthogonal Latin squares, orthogonal arrays, balanced and partially
balanced incomplete block designs. Algebras of association schemes and
relations. Randomization, orthogonal designs, general balance and strata.
(3).
220- ESTIMATION,
HYPOTHESIS TESTING, AND STATISTICAL DECISION
Prerequisites,
Statistics 155 and 165. Bayes procedures for estimation and testing.
Minimax procedures. Unbiased estimators. Unbiased tests and similar
tests. Invariant procedures. Sufficient statistics. Confidence sets.
Large sample theory. Statistical decision theory. Simons. (3).
221- SEQUENTIAL
ANALYSIS
Prerequisites,
Statistics 155 and 165. Hypothesis testing and estimation when the sample
size depends on the observations. Sequential probability ratio tests.
Sequential design of experiments. Optimal stopping. Stochastic approximation.
Simons. (3).
222- NONPARAMETRIC
INFERENCE: RANK-BASED METHODS
Prerequisites,
Statistics 155, 165. Estimation and testing when the functional form
of the population distribution is unknown. Rank, sign, and permutation
tests. Optimum nonparametric tests and estimators, including simple
multivariate problems. Sen. (3).
223- NONPARAMETRIC
INFERENCE: SMOOTHING METHODS
Prerequisites,
Statistics 155, 165. Density and regression estimation when no parametric
model is assumed. Kernel, spline, and orthogonal series methods. Emphasis
on analysis of the smoothing problem and data based smoothing parameter
selectors. Marron. (3).
224- STATISTICAL
LARGE SAMPLE THEORY
Prerequisites:
Statistics 155 and 165 Asymptotically efficient estimators; maximum
likelihood estimators. Asymptotically optimal tests; likelihood ratio
tests. Simons. (3).
225- SUBSAMPLING
TECHNIQUES
Prerequisite,
Statistics 165. Basic subsampling concepts: replicates, empirical c.d.f.,
U-statistics. Subsampling for i.i.d. data: jackknife, typical-values,
bootstrap. Subsampling for dependent or nonidentically distributed data:
blockwise and other methods. Carlstein. (3).
231- ADVANCED
PROBABILITY
Prerequisites,
Statistics 154 and 155. Advanced theoretic course covering topics selected
from: weak convergence theory, central limit theorems, laws of large
numbers, stable laws, random walks, martingales. Kallianpur. (3).
232- STOCHASTIC
PROCESSES
Prerequisites,
Statistics 154 and 155. Advanced theoretic course including topics selected
from: Foundations of stochastic processes, renewal processes, stationary
processes, Markov processes, martingales, point processes. (3).
233- TIME SERIES
ANALYSIS
Prerequisites,
Statistics 185. Analysis of time series data by means of particular
models such as autoregressive and moving average schemes. Spectral theory
for stationary processes and associated methods for inference. Stationarity
testing. Leadbetter. (3).
234- EXTREME
VALUE THEORY
Prerequisites,
Statistics 154 and 155. Classical asymptotic distributional theory for
maxima and order statistics from i.i.d. s equences, including extremal
types theorem, domains of attraction, Poisson properties of high level
exceedances. Extremal properties of stationary stochastic sequences
and continuous time processes. Leadbetter. (3).
235- POINT PROCESSES
Prerequisite,
Statistics 155. Random measures and point processes on general spaces,
general Poisson and related processes, regularity, compounding. Point
processes on the real line, stationarity and Palm distributions, Palm-Khintchine
formulae. Convergence of point processes and related topics. Leadbetter.
(3).
236- STOCHASTIC
ANALYSIS
Prerequisite,
Statistics 154 amd 155, or permission of the instructor. Advanced course
covering topics selected from: semimartingale theory, stochastic integrals,
homogeneous chaos expansions, stochastic differential equations, Malliavin
calculus, infinite dimensional processes, functional central limit theorems,
Feynman-Kac formula, Feynman integral. Applications to filtering theory,
infinite particle systems, quantum mechanics, and stochastic models
in neurophysiology. (3).
252- INFORMATION
THEORY
Prerequisite,
Statistics 164. Transmission of information, entropy, message ensembles,
discrete sources, transmission channels, channel encoding, and decoding
for discrete channels. (3).
253- ERROR CORRECTING
CODES
Prerequisite,
Statistics 212, or permission of the instructor. Linear codes and their
error-correcting capabilities. Hamming codes, Reed-Muller codes, cyclic
codes, Bose-Chaudhuri codes, Goppa codes. Burst error corrections. Majority
logic decoding. (3).
260- MULTIVARIATE
ANALYSIS
Prerequisites,
Statistics 165 and matrices. Multivariate normal distributions. Related
distributions. Tests and confidence intervals. Multivariate analysis
of variance, covariance, and regression. Association between subsets
of a multivariate normal set. Theory of discriminant, canonical, and
factor analysis. (3).
261- ADVANCED
PARAMETRIC MULTIVARIATE ANALYSIS
Prerequisite,
Statistics 260. Distribution problems involved in the normal theory
analysis of general multivariate linear models including the growth
curves. Roy's union-intersection principle and its role in multivariate
analysis. An introduction to zonal polynomials and orthogonal groups.
Sen. (3).
262- NONPARAMETRIC
MULTIVARIATE ANALYSIS
Prerequisite,
Statistics 222. Nonparametric MANOVA. Large sample properties of the
tests and estimates. Robust procedures in general linear models including
the growth curves. Nonparametric classification problems. Sen. (3).
The
following 300-level courses are new or have been offered in recent years.
-
TOPICS
IN THE DESIGN OF EXPERIMENTS AND ELEMENTS OF CODING THEORY , Chakravarti
PATTERN RECOGNITION, Nobel.
DESIGN AND CODING , Chakravarti.
INTRODUCTION TO MATHEMATICAL FINANCE , Ji
DATA-ANALYTIC MODELLINGS AND THEIR APPLICATIONS , Fan
ENVIRONMENTAL
STATISTICS , Smith
INTRODUCTION TO
STOCHASTIC OPTION PRICING THEORY , Kallianpur.
INTRODUCTION TO ESTIMATION AND DETECTION
THEORY, Kallianpur
STATISTICAL COMPUTING, Marron
DESIGN AND STATISTICAL PROCEDURES
FOR INDUSTRIAL EXPERIMENTATION AND CLINICAL TRIALS, Chakravarti
GIBBS RANDOM FIELDS AND CERTAIN STATISTICAL
APPLICATIONS, Ji
TOPICS IN DESIGN AND CODING, Chakravarti
TOPICS IN WEAK CONVERGENCE, MARKOV
PROCESSES AND STOCHASTIC DIFFERENTIAL EQUATIONS, Kallianpur
300- SEMINAR IN STATISTICAL LITERATURE
Prerequisite, Statistics 165. (1).
302- SEMINAR IN STATISTICAL DATA
ANALYSIS
Prerequisite, Statistics 174. (Var.)
310, 311- SEMINAR IN THEORETICAL
STATISTICS
Prerequisite, Statistics 165. (3).
321, 322- SPECIAL PROBLEMS
Prerequisite, permission of the instructor.
(3).
331, 332- ADVANCED RESEARCH
Prerequisite, permission of the instructor.
(3).
393- MASTER'S THESIS
Prerequisite, permission of the student's
adviser. Fall and spring. Staff. (Var.). A minimum of 3 credit
hours of 393 is required for the M.S. degree.
394- DOCTORAL DISSERTATION
Prerequisite, permission of the student's
adviser. Fall and spring. Staff.(Var.). A minimum of 3 credit hours
of 394 is required for the PhD degree.
400- GENERAL REGISTRATION
