Statistical Science

Undergraduate Courses

1301 - Introduction to Statistics
Introduction to collecting observations and measurements, organizing data, variability, and fundamental concepts and principles of decision-making. Emphasis is placed on statistical reasoning and the uses and misuses of statistics.

2301 - Statistics for Modern Business Decisions
A foundation in data analysis and probability models is followed by elementary applications of confidence intervals, hypothesis testing, correlation, and regression. Prerequisite: CEE Math Fundamentals or equivalent.

2331 - Introduction to Statistical Methods
An introduction to statistics for behavioral, biological, and social scientists. Topics include descriptive statistics, probability and inferential statistics including hypothesis testing, analysis of variance, and contingency tables.

4340 - Statistical Methods for Engineers and Applied Scientists (Co-listed as CSE 4340)
Basic concepts of probability and statistics useful in the solution of engineering and applied science problems. Topics: probability, probability distributions, data analysis, sampling distributions, estimation, and simple tests of hypothesis. Prerequisite: MATH 1337 and 1338.

4370 - Survey Sampling
Simple random sampling; stratified, systematic, subsampling; means, variances, confidence limits; finite population correction; sampling from binomial populations. Principles of planning and conducting surveys. Prerequisite: Permission of instructor.

5340 - Probability and Statistics for Scientists and Engineers (Co-listed as CSE 5370)
Introduction to fundamentals of probability and distribution theory, statistical techniques used by engineers and physical scientists. Examples of tests of significance, operating characteristic curve, tests of hypothesis about one and two parameters, estimation, analysis of variance, and the choice of a particular experimental procedure and sample size. Prerequisite: Math 1337, 1338 and 2339, or equivalent.

5344 - Statistical Quality Control (Co-listed as 5364)
Statistics and simple probability are introduced in terms of problems that arise in manufacturing; their application to control of manufacturing processes. Acceptance sampling in terms of standard sampling plans. Prerequisite: STAT (CSE) 4340 or STAT 5340 (CSE 5370).

5371 - Experimental Statistics
A non-calculus development of the fundamental procedures of applied experimental statistics, including tests of hypotheses and interval estimation for the normal, binomial, chi-square and other distributions, and nonparametric tests. prerequisite: Junior standing or permission of instructor.

5372 - Experimental Statistics
Analysis of variance, completely randomized design, randomized complete block designs-nested classifications, factorials; analysis of covariance, simple and multiple linear regressions, and correlation. Prerequisite: STAT 5371.

5374 - Theory of Probability and Statistics

Sums of random variables, sampling distributions, order statistics, estimation, hypothesis testing and its applications. Prerequisite: STAT (CSE) 4340 or STAT 5340 (CSE 5370)

5377 - Statistical Design and Analysis of Experiments
Introduction to statistical principles in the design and analysis of industrial experiments. Completely randomized, randomized complete and incomplete block, latin square, and Plackett-Burman screening designs. Complete and fractional factorial experiments. Descriptive and inferential statistics. Analysis of variance models. Mean comparisons. Prerequisite: Senior standing with a science or engineering major, or permission of instructor.

Graduate courses

6304. COMPUTATIONAL STATISTICS.
This course introduces students to the fundamentals of statistical computing used by both theoretical and applied statisticians in both academics and industry. Subject matter is divided into two areas, simulation experiments and statistical software, and includes generating random deviates from various distributions, analysis of statistical algorithms, an introduction to UNIX, an introduction to S-Plus for data analysis and graphics, interfacing S-Plus to code written in C and/or FORTRAN, and managing and manipulating very large data sets. Prerequisite: STAT 6327 or concurrent enrollment in this course.

6320. QUADRATIC FORMS AND MATRIX COMPUTATIONS.
Statistical distribution theory of quadratic forms of normal variables. Matrix and vector operations as they pertain to the distribution of quadratic forms. Distributions, moments, and independence of quadratic forms. Computer implementation using SAS. Prerequisite: Linear Algebra.

6327. MATHEMATICAL STATISTICS.
Theory of probability distributions. Random variables and functions of random variables. Multivariate and conditional distributions. Sampling distributions; order statistics. Expected value, transformations, approximations. Prerequisite: Advanced Calculus or permission of instructor.

6328. MATHEMATICAL STATISTICS.
Sufficiency and completeness. Unbiased, maximum likelihood and Bayes point estimators, minimizing risk. Confidence sets. Most powerful, uniformly MP and likelihood ratio tests. Large-sample approximations; contingency table analysis. Prerequisite: STAT 6327.

6336. STATISTICAL ANALYSIS.
Analysis of data from one and two samples assuming normal distributions and independent errors. Discussion of paired sample analyses and of nonparametric location tests.

6337. STATISTICAL ANALYSIS.
Emphasis on application of statistical principles in the design of experiments. Complete and fractional factorials, blocking, nesting, replication, randomization. Analysis of data from classical multifactor experimental designs with fixed and random effects. Multiple comparisons and contrasts of main effects and interactions. Introduction to regression analysis. Prerequisite: STAT 6336.

6342. ADVANCED STATISTICAL QUALITY CONTROL.
Investigate statistical methods and management principles useful for understanding and improving measurable performance in human endeavors. Develop a “statistical thinking” foundation through the evaluation of case studies and class labs. Prerequisite: STAT 4340/CSE 4340, or STAT 5340/CSE 5370, or STAT 5371; or Corequisite: STAT 6327 or 6336.

6345. LINEAR REGRESSION.
The classical tools of linear regression based upon least squares estimation and inference through the assumption of normally distributed errors. Topics in model formulation, data transformations, variable selection, and regression diagnostics for influential observations. Collinear predictors and biased estimation. Survey of alternatives to least squares. Prerequisite: STAT 6320 and 6337.

6346. ADVANCED REGRESSION ANALYSIS.
Nonlinear least-squares estimation. Theory and applications of generalized linear models. Estimation, asymptotic distribution theory, and tests for model parameters. Topics in spatial statistical modeling, including variogram estimation and kriging. Prerequisites: STAT 6345 or permission of instructor.

6350.  ANALYSIS OF LIFETIME DATA.
Statistically based methods for analysis of life testing and failure data from complete and censored samples.  Topics include: statistical lifetime distributions; types of censoring, probability and other graphical techniques; nonparametric and parametric estimation methods and lifetime data regression.

6355. APPLIED MULTIVARIATE ANALYSIS.
Statistical methods of analysis of multivariate data, tests and estimation of multivariate normal parameters; Hotelling’s T2, discriminant analysis, canonical correlation, principal components, and factor analysis. Applications are emphasized. Prerequisites: STAT 6337 and 6320.

6358. TOPICS IN BIOSTATISTICS.
Introduction to various statistical methods that are widely used in the biosciences, especially biomedical research. Subject matter includes survival analysis, contingency tables, logistic regression, analysis of longitudinal data, design of clinical experiments, epidemiology, and statistical genetics; topics may vary with instructor. Prerequisite: STAT 6328 or permission of instructor.

6363. TIME SERIES ANALYSIS.
Statistical methods of analyzing time series. Autocorrelation function and spectrum. Autoregressive and moving average processes. More general models, forecasting, stochastic model building. Prerequisite: Permission of instructor.

6366. STATISTICAL CONSULTING.
Apprenticeship under an experienced consultant, with exposure to real problems handled by the Center for Statistical Consulting and Research. Between four to six hours per week will be spent in consultation sessions and seminars. In addition to a variety of technical statistical issues the class will study the existing literature on the nonstatistical aspects of the consulting endeavor.

6370 (CSE 6370). STOCHASTIC MODELS.
Model building with stochastic processes in applied sciences. Phenomena with uncertain outcomes are formulated as stochastic models and their properties are analyzed. Some specific problems discussed come from areas such as population growth, queueing, reliability, time series, and social and behavioral processes. Statistical properties of the models are emphasized. Prerequisites: STAT 5340/CSE 5370 and graduate standing.

6371. PROBABILITY THEORY.
An introduction to measure theoretic probability. Random variables, expectation, conditional expectation, characteristic functions. Prerequisite: STAT 6327 or permission of instructor.

6372 (CSE 6372). QUEUEING THEORY.
Queueing theory provides the theoretical basis for the analysis of stochastic service systems. The underlying stochastic processes are point processes of which Markov and renewal processes are two major examples. The emphasis of the course is in the formulation of queueing models and their behavioral and statistical analyses using Markov and renewal techniques. Prerequisite: An introductory course in Stochastic Processes (e.g. STAT 6370/CSE 6370, STAT 6376, 6379, EE 5306).

6375. SEQUENTIAL ANALYSIS.

 Statistical Inference when sample size is not predetermined. Stopping rules, sequential probability ratio tests, composite hypotheses. Bayes rules, sequential estimation. Prerequisite: STAT 6328.

6376. STOCHASTIC PROCESSES

.Random walk, Markov processes, Poisson prcesses, waiting times, spectral density functions, applications to random noise problems. Prerequisite: STAT 6327.

6377. MULTIVARIATE CATEGORICAL DATA.

 Structural models for counting data: The general log-linear model for contingency tables is introduced along with likelihood-ratio tests, hierarchical models, and partitioning of likelihood-ratio statistics. Prerequisites: STAT 6328 and 6337, or permission of instructor.

6378. MULTIVARIATE ANALYSIS.
Theory and inference in the multivariate normal distribution. Regression, correlation, Wishart distribution, Hotelling's T² , MANOVA and discriminant analysis. Prerequisite: STAT 6320, and 6328 or 6381.

6379. INTRODUCTION TO MARKOV PROCESSES

Branching processes, recurrent events, random walk, finite Markov chains, simplest time-dependent stochastic processes. Prerequisite: STAT 6327 or 6370/CSE/6370.6380. MATHEMATICAL THEORY OF SAMPLING. Theorems concerning simple random sampling, stratified random sampling, cluster sampling, unequal probability sampling, ratio estimates, regression estimates, etc. Prerequisite: STAT 6328..

6381. THEORY OF LINEAR MODELS.
Theory of the general linear model; estimability and testability. Theory of analysis of fixed, random and mixed models. Prerequisite: STAT 6328, 6337, and 6320.

6382. THEORY OF LINEAR MODELS II.

Variance component models, mixed models, intro-block analysis, incomplete block designs and factorials, fractional replicates. Prerequisite: STAT 6381.

6385. SURVEY OF NONPARAMETRIC STATISTICS.
Topics include robust and distribution-free techniques; order statistics, EDF statistics, quantiles, asymptotic distributions and tolerance intervals; linear rank statistics for one, two, and several sample problems involving location and scale; runs; multiple comparison; rank correlation; and asymptotic relative efficiency. Prerequisite: STAT 6328.

6386. NONPARAMETRIC STATISTICS.

Continuation of topics covered in STAT 6385, including linear rank statistics and asymptotic relative efficiency. Additional topics include U-Statistics, robustness, M-estimation, minimum distance estimation, adaptive procedures, density estimation, aligned ranks, jackknifing, and bootstrapping. Prerequisite: STAT 6385.

6388. LARGE SAMPLE THEORY.
Limit theorems useful in mathematical statistics. The foundation of asymptotic theory in statistics including modes of convergence, laws of large numbers and the central limit theorem. Systematic coverage of useful representations of certain basic statistics and large sample optimality of maximum likelihood procedures. Prerequisites: STAT 6328 and 6371.

6390. DECISION THEORY AND BAYESIAN STATISITCS..

The decision theory and Bayesian approaches to statistics. Decision rules, admissibility, complete classes, Bayes and minimax rule. Likelihood principle, empirical Bayes rules, and personal probability. Prerequisite: STAT 6328.6395. SELECTED TOPICS IN STATISTICS Discussion of statistical theory and methodology on specialized topics of interest.

7100. Seminar
7300. Seminar

7327. ADVANCED STATISTICAL INFERENCE.
Topics in statistical inference; estimation (point and interval estimates, Bayesian and likelihood); tests of hypotheses (invariant, unbiased, most powerful, conditional, Bayesian); large-sample theory for multiparameter problems. Prerequisite: STAT 6371.

7362. ADVANCED SPECIAL TOPICS. Lectures and readings on state-of-the-art statistical issues using emerging statistical theory and methods.
8196, 8396: Dissertation
8197, 8397:, 8697: Dissertation
8198, 8398, 8698: Dissertation
8199, 8399, 8699: Dissertation