Graduate Course Descriptions

Credits: 3

Prereq: STA 2023 or STA 4322 or STA 5328 or STA 6126 or STA 6166

Design and analysis of sample surveys. Sources of error; questionaire design; simple random, stratified, systematic, and cluster sampling; plus practical application of these concepts.

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.

Credits: 3

Prereq: STA 4321 or STA 5325

Mathematical foundations of point estimation, confidence intervals, tests of hypotheses, linear models and analysis of variance.

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.

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.

Credits: 3

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.

Credits: 3

Prereq: STA 4321 or STA 5325

Mathematical foundations of elementary stochastic processes; Poisson processes; Markov chains; branching and renewal processes.

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.

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.

Credits: 3

Prereq: STA 6126

Further topics in multiple regression, model building, analysis of variance, analysis of covariance, multivariate analysis of categorical data.

Credits: 3

Prereq: None

Statistical inference based on t, F, and X2 tests. Analysis of variance for basic experimental designs. Factorial experiments. Regression analysis and analysis of covariance.

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.

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.

Credits: 3

Prereq: STA 6327

Survival analysis, Kaplan-Meier estimates, proportional hazards model, related tests, phase I, II, and III clinical trials, designs and protocols.

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.

Credits: 2

Prereq: None

Choosing the research objective, determining the type of data to collect, repeated measures and blocking, choosing the sample and the randomization technique, designing a data collection form. Applications to biomedical data.

Credits: 3

Prereq: STA 6200

Introduction to the most commonly used statistical analyses for evaluating research data, with application to the biomedical sciences. Emphasis on choosing the appropriate procedure and evaulauing the results properly, rather than on the computational aspects of the procedures.

Credits: 3

Prereq: STA 4322

Overview of normal theory inference, nonparametric, and categorical data methods; basic concepts of experimental design; analysis of variance; introduction to factorial and nested experiments.

Credits: 3

Prereq: STA 6207

Simple linear regression; multiple regression; model selection residual analysis; influence diagnostics; multicollinearity; ANOVA and regression; generalized linear models; nonlinear regression.

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.

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.

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.

Credits: 3

Prereq: STA 6246 and STA 6207 and STA 6208 and STA6209

First and second order response surface designs and models. The objectives of a response surface investigation. The determination of optimum conditions for response surface models. The integrated mean square error criterion for the choice of a design. Minimum bias estimation designs. The analysis of multiresponse experiments. Designs for nonlinear models. Some advanced topics in unbalanced mixed models.

Credits: 3

Prereq: STA 6209 and STA 6246

Estimation of variance components. Best linear unbiased predication of random effects. Measures of imbalance. Exact tests for unbalanced random and mixed-effects models. Generalized P-values.

Credits: 3

Prereq: STA 6327

Double sampling procedures, the sequential probability ratio tests, sequential tests for composite hypotheses, sequential estimation and confidence intervals.

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.

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.

Credits: 3

Prereq: MAC 3313 and STA STA 6208

Basic theory of determinants, inverses and generalized inverses, eigenvalues and eigenvectors; applications of partitioned matrices; diagonalization and decomposition theorems; applications in least squares.

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.

Credits: 3

Prereq: STA 6466

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.

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.

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.

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.

Credits: 3

Prereq: statistical theory of distributions, basic analysis of variance; coreq: theory of statistical estimation and testing.

Statistical techniques used in modern industry, including variance components analysis, control charting, estimation of process characteristics, evolutionary operation, fraction, factorials, screening experiments.

Credits: 3

Prereq: STA 6166 or consent of instructor.

Bivariate relationship: matrix algebra; review of multiple regression and correlation; part and partial correlation; canonical correlation; discriminant analysis and classification; cluster analysis; factor analysis.

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

Discrete time and state Markov process. Ergodic theory.

Credits: 4

Prereq: STA 6826

Continuous time Markov processes. The Poisson and allied processes. The Kolmogorov equations. Renewal theory.

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.

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.

Credits: 1-4; max: 6

Prereq: permission of department

Special problems in research methods, sampling methods, and experimental designs.

Credits: 1-4; max: 10

Prereq: Permission of department

Special topics designed to meet the needs and interests of individual students.

Credits: 1-5; max: 5

Prereq: Premission of department

S/U

Credits: (1-3; max: 8)

Prereq: permission of graduate adviser.

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

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

Credits: 1-5; max: 5

Prereq: Permission of department

S/U

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

Credits: 1-15

Prereq: Permission of Department

S/U

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 6467

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.

Credits: 3

Prereq: STA 6327

Decision rules and risk functions. Sufficiency, Minimax, and Bayes rules for estimation of location and scale parameters.

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.

Credits: 3

Prereq: STA 6327 and STA 6208 and STA 6505

Models for multinomial responses such as original data, models for matched pairs and more complex types of repeated categorical measurement data, and small-sample and large-sample theory for parametric model fitting and recent research in categorical data analysis.

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

Credits: 1-15

Prereq: Permission of Department

S/U

Credits: 3

Prereq: STA 4322

Numerical sequences and series, limits, continuity, differentiation, integration, series of functions. Applications to probability and statistics stressed.