Courses in Statistics (STAT)

Undergraduate Level

Upper-Division Courses

STAT 302 Elementary Statistical Methods II (3 cr.) P: 301 or equivalent. Continuation of 301. Multiple regression and analysis of variance, with emphasis on statistical inference and applications to various fields.

STAT 311 Introductory Probability (3 cr.) P: MATH 261 or equivalent. Fall. Fundamental axioms and laws of probability; finite sample spaces and combinatorial probability; conditional probability; Bayes theorem; independence; discrete and continuous random variables; univariate and bivariate distributions; binomial, negative binomial, Poisson, normal, and gamma probability models; mathematical expectation; moments and moment generating functions.

STAT 490 Topics in Statistics for Undergraduates (1-5 cr.) Supervised reading and reports in various fields.

Undergraduate and Graduate Level

STAT 512 Applied Regression Analysis (3 cr.) P: 511. Inference in simple and multiple linear regression, residual analysis, transformations, polynomial regression, model building with real data, nonlinear regression. One-way and two-way analysis of variance. Use of existing statistical computing packages.

STAT 513 Statistical Quality Control (3 cr.) P: 511. Control charts and acceptance sampling, standard acceptance plans, continuous sampling plans, sequential analysis, statistics of combinations, and some nonparametric methods. Use of existing statistical computing packages.

STAT 514 Designs of Experiments (3 cr.) P: 512. Fundamentals, completely randomized design, randomized complete blocks. Latin squares, multiclassification, factorial, nested factorial, incomplete blocks, fractional replications, confounding, general mixed factorial, split-plot and optimum design. Use of existing statistical computing packages.

STAT 515 Statistical Consulting Problems
(1-3 cr.) P: Consent of advisor. Consultation on real-world problems involving statistical analysis under the guidance of a faculty member. A detailed written report and an oral presentation are required.

STAT 516 Basic Probability and Applications (3 cr.) P: MATH 262 or equivalent. A first course in probability intended to serve as a foundation for statistics and other applications. Intuitive background; sample spaces and random variables; joint, conditional, and marginal distributions; special distributions of statistical importance; moments and moment generating functions; statement and application of limit theorems; introduction to Markov chains.

STAT 517 Statistical Inference (3 cr.) P: 511 or 516. A basic course in statistical theory covering standard statistical methods and their applications. Includes unbiased, maximum likelihood, and moment estimation; confidence intervals and regions; testing hypotheses for standard distributions and contingency tables; introduction to nonparametric tests and linear regression.

STAT 519 Introduction to Probability (MATH 519) (3 cr.) P: MATH 262. Algebra of sets, sample spaces, combinatorial problems, conditional probability, independence, random variables, distribution functions, characteristic functions, special discrete and continuous distributions, distributions of function of random variables, limit theorems.

STAT 520 Time Series and Applications (3 cr.) P: 519. A first course in stationary time series with applications in engineering, economics, and physical sciences. Stationarity, autocovariance function and spectrum; integral representation of a stationary time series and interpretation; linear filtering; transfer function models; estimation of spectrum; multivariate time series. Use of existing statistical computing packages.

STAT 522 Sampling and Survey Techniques (3 cr.) P: 512 or equivalent. Survey designs; simple random, stratified, and systematic samples; systems of sampling; methods of estimation; ratio and regression estimates; costs.

STAT 523 Categorical Data Analysis (3 cr.) P: 528 or equivalent, or consent of instructor. Models generating binary and categorical response data, two-way classification tables, measures of association and agreement, goodness-of-fit tests, testing independence, large sample properties. General linear models, logistic regression, probit and extreme value models. Loglinear models in two and higher dimensions; maximum likelihood estimation, testing goodness-of-fit, partitioning chi-square, models for ordinal data. Model building, selection, and diagnostics. Other related topics as time permits. Computer applications using SAS.

STAT 524 Applied Multivariate Analysis (3 cr.) P: 528 or equivalent, or consent of instructor. Extension of univariate tests in normal populations to the multivariate case, equality of covariance matrices, multivariate analysis of variance, discriminant analysis and misclassification errors, canonical correlation, principal components, factor analysis. Strong emphasis on the use of existing computer programs.

STAT 525 Intermediate Statistical Methodology (3 cr.) C: 528 or equivalent, or consent of instructor. Generalized linear models, likelihood methods for data analysis, diagnostic methods for assessing model assumptions. Methods covered include multiple regression, analysis of variance for completely randomized designs, binary and categorical response models, and hierarchical loglinear models for contingency tables.

STAT 528 Mathematical Statistics I (3 cr.) P: 519 or equivalent. Distributions of functions of several variables; chi-square, Student’s-t, F, and beta distributions. Distributions of order statistics, multivariate normal distribution. Quadratic forms, normal linear model with applications, limit theorems and applications.

STAT 529 Bayesian Statistics and Applied Decision Theory (3 cr.) P: A course in statistics. C: 528 or equivalent. Foundation of statistical analysis, Bayesian and decision theoretic formulation of problems; construction of utility functions and quantifications of prior information; methods of Bayesian decision and inference, with applications; empirical Bayes; combination of evidence; game theory and minimax rules; Bayesian design and sequential analysis.

STAT 530 Mathematical Statistics II (3 cr.) P: 528. Sufficiency and completeness, the exponential family of distributions, theory of point estimation, Cramer-Rao inequality, Rao-Blackwell theorem with applications, maximum likelihood estimation, asymptotic distributions of ML estimators, hypothesis testing, Neyman-Pearson lemma, UMP tests, generalized likelihood ratio test, asymptotic distribution of the GLR test, sequential probability ratio test.

STAT 532 Elements of Stochastic Processes (MATH 532) (3 cr.) P: 519 or equivalent. A basic course in stochastic models including discrete and continuous time processes, Markov chains, and Brownian motion. Introduction to topics such as Gaussian processes, queues and renewal processes, and Poisson processes. Application to economic models, epidemic models, and reliability problems.

STAT 533 Nonparametric Statistics (3 cr.) P: 519 or equivalent. Binomial test for dichotomous data, confidence intervals for proportions, order statistics, one-sample signed Wilcoxon rank test, two-sample Wilcoxon test, two-sample rank tests for dispersion, Kruskal-Wallis test for one-way layout. Runs test and Kendall test for independence, one- and two-sample Kolmogorov-Smirnov tests, nonparametric regression.

STAT 598 Topics in Statistical Methods
(1-3 cr.) P: Consent of instructor. Directed study and reports for students who wish to undertake individual reading and study on approved topics.