Department of Statistics

Graduate Course Descriptions

STA 5223--Applied Sample Survey Methods (Fall in even numbered years)
Credits: 3
Prereq: STA 4321 and either STA 2023 or STA 3032 or STA 4322
Design and analysis of sample surveys. Sources of error; questionaire design; simple random, stratified, systematic, and cluster sampling; plus practical application of these concepts.

STA 5325--Fundamentals of Probability (Fall, Spring, Summer)
Credits: 3
Prereq: MAC 2313 and Intro. Stat.
Probability, counting rules, conditional probablity, independence, Bayes' Rule. Discrete and continuous distributions, means, variances, moment generating functions. Multivariate probability distributions, marginal and conditional distributions, covariance. Distributions of functions of random variables.

STA 5328--Fundamentals of Statistical Theory (Fall, Spring, Summer)
Credits: 3
Prereq: STA 4321 or STA 5325
Mathematical foundations of point estimation, confidence intervals, tests of hypotheses, linear models and analysis of variance.

STA 5503--Categorical Data Methods (Spring)
Credits: 3
Prereq: STA 3024 or STA 3032 or STA 4210 or STA 4322 or STA 6127 or STA 6167
Intended for graduate students not majoring in statistics. Description and inference using proportions and odds ratios, multi-way contingency tables, logistic regression and other generalized linear models, and loglinear models applications.

STA 5507--Applied Nonparametric Methods (Fall in odd numbered years)
Credits: 3
Prereq: STA 2023 or STA 3032 or STA 4210 or STA 4322 or STA 6126 or STA 6166
Introduction to nonparametric statistics, including one and two sample testing and estimation methods, one- and two-way layout models, and correlation and regression models.

STA 5701--Applied Multivariate Methods (Spring in odd numbered years)
Credits: 3
Prereq: STA 3032 or STA 4210 or STA 4322 or STA 6167 and either MAS 4105 or the equivalent
Review of matrix theory, univariate normal, t, chi-squared, F and multivariate normal distributions. Inference about multivariate means including Hotelling's T squared, multivariate analysis of variance, multivariate regression and multivariate repeated measures. Inference about covariance structure including principal components, factor analysis and cannonical correlation. Multivariate classification techniques including discriminant and cluster analysis. Additional topics at the discretion of the instructor, time permitting.

STA 5823--Stochastic Process Methods (Fall in even numbered years)
Credits: 3
Prereq: STA 4321 or STA 5325
Mathematical foundations of elementary stochastic processes; Poisson processes; Markov chains; branching and renewal processes.

STA 6092--Applied Statistical Practice (See Schedule of Graduate Major Course Offerings)
Credits: 3
Prereq: STA 6207 and STA 6208
Introduction to communication, management, organizational, computational, and statistical thinking skills necessary to consulting in statistics. Integration of graphical and numerical computing tools, research design concepts, data summary and statistical inference methods.

STA 6126 --Statistical Methods in Social Research I (Fall, Spring)
Credits: 3
Prereq: None
Descriptive statistics, estimation, significance tests, two-sample comparisons, methods for nominal and ordinal data, regression and correlation, introduction to multiple regression.

STA 6127--Statistical Methods in Social Research II (Spring)
Credits: 3
Prereq: STA 6126
Further topics in multiple regression, model building, analysis of variance, analysis of covariance, multivariate analysis of categorical data.

STA 6166--Statistical Methods in Research I (Fall, Spring, Summer A)
Credits: 3
Prereq: STA 2023
Statistical inference based on t, F, and X2 tests. Analysis of variance for basic experimental designs. Factorial experiments. Regression analysis and analysis of covariance.

STA 6167--Statistical Methods in Research II (Spring, Summer B)
Credits: 3
Prereq: STA 6166
Analysis of split-plot and nested designs with incomplete blocks, confounding and fractional replications. Analysis of count data. Nonparametric methods.

STA 6176--Introduction to Biostatistics (Spring)
Credits: 3
Prereq: STA 6207 and STA 6326
Analysis of epidemiological studies, measures of morbidity and mortality, methods for rates and proportions, bioassay, longitudinal data analysis.

STA 6177--Survival Analysis (Fall)
Credits: 3
Prereq: STA 6327
Survival analysis, Kaplan-Meier estimates, proportional hazards model.

Credits: 3
Prereq: STA 6327
Biological and molecular basis. Likelihood ratio test, multinomial distribution and Bailey's theorem. Linkage analysis of qualitative traits. Twin and sibling studies. Computation of kinship coefficient by matrix method. Mapping of quantitative trait loci by EM algorithm. Heritability. Breeding value predication using flanking markers with variance component analysis. Linkage disequilibrium analysis for gene mapping. Forensic genetics using Bayes' formula. Genetic counseling. Gene pattern matching and construction of evolutionary trees by cluster analysis.

STA 6207--Regression Analysis (Fall)
Credits: 3
Prereq: STA 4322
Simple linear regression; multiple regression; model selection residual analysis; influence diagnostics; multicollinearity; ANOVA and regression; generalized linear models; nonlinear regression.

STA 6208--Basic Design and Analysis of Experiments (Spring)
Credits: 3
Prereq: STA 6207
Overview of normal theory inference, nonparametric, and categorical data methods; basic concepts of experimental design; analysis of variance; introduction to factorial and nested experiments.

STA 6209--Design and Analysis of Experiments (Spring)
Credits: 3
Prereq: STA 6208
Tests of assumptions; block designs; control of two-way heterogeneity; cross over designs; factorial experiments; fractional factorials; analysis of "messy" data.

STA 6226--Sampling Theory and Application (See Schedule of Graduate Major Course Offerings)
Credits: 3
Prereq: STA 6327 or consent of instructor
Theory and application of commonly used sampling techniques; simple random sample, cluster, ratio, regression, stratified, multistage, and systematic samples. Special topics include wildlife surveys, non-sampling error adjustment, categorical data analysis, and practical survey examples.

STA 6246--Theory of Linear Models (Fall)
Credits: 3
Prereq: STA 6208 and STA 6327 and STA 6329
Theory for analysis of linear models in univariate data; distributions of quadratic forms; full rank linear models; fixed effect models of less than full rank; balanced random and mixed models; unbalanced random and mixed models.

STA 6326--Introduction to Theoretical Statistics I (Fall)
Credits: 3
Prereq: MAC 2313
Theory of probability. Probability spaces, continuous and discrete distributions, functions of random variables, multivariate distributions, expectation, conditional expectation, central limit theorem, useful convergence results, sampling distributions, distributions of order statistics, empirical distribution function.

STA 6327--Introduction to Theoretical Statistics II (Spring)
Credits: 3
Prereq: STA 6326
Estimation and hypothesis testing. Sufficiency, information, estimation, maximum likelihood, confidence intervals, uniformly most powerful tests, likelihood ratio tests, sequential testing, univariate normal inference, decision theory, analysis of categorical data.

STA 6329--Matrix Algebra and Statistical Computing (Fall)
Credits: 3
Prereq: MAC 3313
Basic theory of determinants, inverses and generalized inverses, eigenvalues and eigenvectors; applications of partitioned matrices; diagonalization and decomposition theorems; applications in least squares.

STA 6505--Analysis of Categorical Data (See Schedule of Graduate Major Course Offerings)
Credits: 3
Prereq: STA 6327 and STA 6207 or consent of instructor.
Varieties of categorical data, cross-classification tables, tests for independence. Measures of association. Loglinear models for multi-dimensional tables. Logit models and analogies with regression. Specialized methods for ordinal data.

STA 6526--Nonparametric Statistics (See Schedule of Graduate Major Course Offerings)
Credits: 3
Prereq: STA 6327 or consent of instructor.
Inference based on rank statistics-- one, two and k-sample problems, correlation and regression problems and analysis of contingency tables. Conditionally distribution-free rank tests. Pitman asymptotic relative efficiency.

STA 6707--Analysis of Multivariate Data (See Schedule of Graduate Major Course Offerings)
Credits: 3
Prereq: STA 6208 and facility in a computer language.
Techniques for analyzing multivariate data. Emphasis on MANOVA and tests on the structure of the dispersion matrix. Topics will include discriminant, factor, profile, and cluster analyses.

Credits: 4
Prereq: STA 6246 or consent of instructor.
Singular transformations and the generalized Jacobian. The multivariate normal distribution, Wishart distribution, and the U distribution. Distribution of the latent roots of one Wishart matrix in the metric of another. Noncentral counterparts of these distributions--an introduction to zonal polynomials. Distributions of variables constrained to lie on a sphere or a simplex. The resultant and its usage in analysis of directional data.

Credits: 3
Prereq: STA 6327 or STA 6326
Discrete time and state Markov process. Ergodic theory.

STA 6827--Stochastic Processes II (See Schedule of Graduate Major Course Offerings)
Credits: 4
Prereq: STA 6826
Continuous time Markov processes. The Poisson and allied processes. The Kolmogorov equations. Renewal theory.

STA 6857--Applied Time Series Analysis (See Schedule of Graduate Major Course Offerings)
Credits: 3
Prereq: STA 4322 or STA 5328 and a basic computer language.
Linear time series model building, spectral density estimation, analysis of nonstationary data, SAS package on Box and Jenkins model building and forecasting. Case studies in recent literature will be discussed.

STA 6866--Monte Carlo Statistical Methods
Credits: 3
Prereq: STA 6208 and STA 6327
Random-variable generation, accept-reject methods. Monte Carlo Optimization, Markov Chain Methods, diagnostic tools, programming in R and WinBugs. Provide an introduction to statistical methods based on Monte Carlo Methods which have become a standard for statisticians today.

Credits: 3
Prereq: STA 6327
Foundations of stationary time series, distributions of sample autocorrelations, partial autocorrelation, spectral density, time series regression, and special topics in recent time series research.

STA 6905--Individual Work (Arrange)
Credits: 1-4; max: 10
Prereq: Permission of department
Special topics designed to meet the needs and interests of individual students.

STA 6910--Supervised Research (Arrange)
Credits: 1-5; max: 5
Prereq: Premission of department
S/U

STA 6934--Special Topics in Statistics (See Schedule of Graduate Major Course Offerings)
Credits: (1-3; max: 8)
Prereq: permission of graduate adviser.

STA 6937--Seminar: Current Topics in Statistics
Credits: 1-3; max: 6
Prereq: Permission of department
Discussion of current research topics in statistics in statistics not covered in regular courses. S/U

STA 6938--Seminar
Credits: 1; max: 15
Prereq: Permission of department
Special topics of an advanced nature suitable for seminar treatment but not given in regular courses. S/U

STA 6940--Supervised Teaching (Arrange)
Credits: 1-5; max: 5
Prereq: Permission of department
S/U

STA 6942--Internship (Fall, Spring, Summer)
Credits: 1-3; max: 3
Prereq: STA 6208 or equivalent and permission of graduate coordinator
Supervised statistical consulting involving the planning and/or analysis of research data. Whenever possible, the student will meet with the researcher. Supervision by a faculty member or delegated authority. Post internship report is requirecd. S/U

STA 6971--Research for Master's Thesis (Arrange)
Credits: 1-15
Prereq: Permission of Department
S/U

Credits: 3
Prereq: STA 6207, STA 6327, and STA 7467
Theoretical development of statistical methods for analyzing life history data, including censored data and truncated data. Topics covered include: Kaplan-Meier estimator, k-sample tests, proportional hazards regression, and the asymptotic theory associated with all these. Throughout, the counting process approach to survival analysis will be used. A student who takes this course should have had a year-long sequence in probability that covers martingales and the Lindeberg-Feller theorem.

STA 7249--Generalized Linear Models (See Schedule of Graduate Major Course Offerings)
Credits: 3
Prereq: STA 6207 and STA 6208 and STA 6327
Fitting of generalized linear models, diagnostics, asymptotic theory, overdispersion, estimating equations, mixed models, generalized additive models, smoothing.

Credits: 3
Prereq: STA 7467
Review of different models of convergence. Cramer-Wold device. Multivariate CLT. Asymptotic theory of empirical distribution and sample quantiles. Bahadur's representation. Asymptotic theory of sample moments. Delta method and its multiparameter generalization. Variance stabilizing transformation. U-statistics: asymptotic theory and its statistical applications. Hoeffding's decomposition. Asymptotic theory of maximum likelihood estimation. Wald's consistency theorem for MLE. Asymptotic normality and efficiency. Asymptotic theory of GLRTs. Statistical applications: asymptotic theory or categorical data, linear models, and generalized linear models.

STA 7346--Statistical Inference I (Fall)
Credits: 3
Prereq: STA 6327
Decision rules and risk functions. Sufficiency, Minimax, and Bayes rules for estimation of location and scale parameters.

STA 7347--Statistical Inference II (Spring)
Credits: 3
Prereq: STA 7346
Bayesian statistical inference. Inference using large samples. Relative efficiencies of tests and estimates with special reference to Pitman and Bahadur efficiencies.

STA 7348--Bayesian Theory Statistics
Credits: 3
Prereq: permission of graduate adviser.
The objective of the Bayesian Theory course is to provide students with a solid foundation of the theory underlying the Bayesian paradigm. In particular, we will discuss issues related to selection of priors, Bayesian inference both exact and asymptotic, Bayesian model selection, high dimensional problems, and if time permits, some issues related to Bayesian robustness.

STA 7466--Probability Theory I (Fall)
Credits: 3
Prereq: MAA 5228 or equivalent
Measure and probability spaces; random variables; distribution functions; abstract Lebesgue and Stieltjes integration; monotone; dominated, Cauchy, and mean convergence; Fubini and Radon-Nikodym theorems; zero-one laws.

STA 7467--Probability Theory II (Spring)
Credits: 3
Prereq: STA 7466
Summability of independent random variables, laws of large numbers, convergence in distribution, characteristic functions, uniqueness and continuity theorems, the Lindeberg-Feller central limit theorem, degenerate convergence criterion.

STA 7527--Theory of Nonparametric Statistics (See Schedule of Graduate Major Course Offerings)
Credits: 3
Prereq: STA 6526 or consent of instructor
Theoretical foundations of nonparametric statistics: theory of U-statistics, Noether's theorem and Pitman asymptotic relative efficiency, estimation and hypothesis testing with one and two sample models, theory of linear rank statistics, applications to general linear models analyses.

STA 7828--Topics in Stochastic Processes
Credits: 3
Prereq: permission of graduate adviser.
Topics to be covered may include: branching processes, Brownian motion, continuous state space Markov chains, di usion processes, Markov chain Monte Carlo, martingales,point processes, renewal processes, stationary processes, stochastic calculus, stochastic dfferential equations.

STA 7979--Advanced Research (Arrange)
Credits: 1-12
Prereq: Permission of Department
Research for doctoral students before admission to candidacy. Designed for students with a master's degree in the field of study or for student who have been accepted for a doctoral program. Not open to students who have been admitted to candidacy. S/U

STA 7980--Research for Doctoral Dissertation (Arrange)
Credits: 1-15
Prereq: Permission of Department
S/U

 

**NOTE: A Schedule of Courses is also kept in the Graduate Catalog kept by the Office of Research and Graduate Programs