Statistics Course Descriptions
Undergraduate and Graduate Courses
STOR 151-BASIC CONCEPTS OF STATISTICS AND DATA ANALYSIS I-
Prerequistite: MATH 110 (or exemption). Elementary introduction to statistical reasoning, including sampling, elementary probability, statistical inference, and data analysis. STOR 151 may not be taken for credit by students who have a credit for ECON 400 or PSYC 210. (3)
STOR 155-INTRODUCTION TO STATISTICS -
Prerequisite: MATH 110 (or exemption). Data analysis; correlation and regression; sampling and experimental design; basic probability (random variables, expected values, normal and binomial distributions); hypothesis testing and confidence intervals for means, proportions, and regression parameters; use of spreadsheet software. (3)
STOR 455-STATISTICAL METHODS I -
Prerequisite: STOR 155 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. (3)
STOR 456- STATISTICAL METHODS II -
Prerequisite: STOR 455. Topics selected from: design of experiments; sample surveys; nonparametrics; time-series; multivariate analysis; contingency tables; logistic regression; simulation. Use of statistical software packages. Spring. Pipiras, Smith. (3)
STOR 358- SAMPLE SURVEY METHODOLOGY (BIOS 664) -
Prerequisite: STOR 456 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)
STOR 435- INTRODUCTION TO PROBABILITY (MATH 535) -
Prerequisite: MATH 233. 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, Budhiraja, Nobel. (3)
STOR 555- MATHEMATICAL STATISTICS -
Prerequisite: STOR 435 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 only. Carlstein, Kelly. (3)
Graduate
STOR 634- MEASURE AND INTEGRATION -
Prerequisite: real analysis. Lebesgue and abstract measure and integration, convergence theorems, differentiation. Radon-Nikodym theorem, product measures. Fubini theorems. Lp spaces. Fall. Leadbetter, Pipiras, Budhiraja. (3).
STOR 635- PROBABILITY-
Prerequisite: STOR 634 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. Leadbetter, Pipiras, Budhiraja. (3)
STOR 654- STATISTICAL THEORY I -
Prerequisite: advanced calculus. Probability spaces; Random variables, distributions, expectation; Conditioning; Generating functions; Limit theorems: LLN, CLT, Slutzky, delta-method, big- and little O notation, convergence in probability; Inequalities; Distribution theory: normal, chi-squared, beta, gamma, Cauchy, other multivariate distributions; Multivariate Normal distribution. Fall. Nobel, Hannig. (3)
STOR 655- STATISTICAL THEORY II -
Prerequisite: STOR 654 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. Spring. (3)
STOR 664- 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. Carlstein, Smith, Liu (3)
STOR 665- APPLIED STATISTICS II -
Prerequisite: STOR 664 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. Shen. (3)
STOR 734- STOCHASTIC PROCESSES - Equivalent to STOR 641
Prerequisites: STOR 435 and permission of instructor. Discrete Markov chains; Continuous Markov chains: Poisson, birth-death, etc.; Stationary processes. Fall. Ji, Nobel, Kulkarni. (3).
STOR 754- TIME SERIES AND MULTIVARIATE ANALYSIS -
Prerequisite: STOR 435. 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, Smith, Sen. (3)
STOR 765- 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 and Spring. Marron, Smith. (3 credits for one year)
STOR 756- 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. (3)
STOR 757- BAYESIAN STATISTICS AND GENERALIZED LINEAR MODELS -
Corequisites: STOR 664 and 655, 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. Smith (3)
Cross-Listed Courses in Other Departments
STOR 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).
STOR 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).
Advanced Graduate
STOR 755- ESTIMATION, HYPOTHESIS TESTING, AND STATISTICAL DECISION -
Prerequisites: STOR 635 and 655. 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. Kelly, Nobel. (3).
STOR 851- SEQUENTIAL ANALYSIS -
Prerequisites: STOR 635 and 655. Hypothesis testing and estimation when the sample size depends on the observations. Sequential probability ratio tests. Sequential design of experiments. Optimal stopping. Stochastic approximation. (3).
STOR 852- NONPARAMETRIC INFERENCE: RANK-BASED METHODS -
Prerequisites: STOR 635 and 655. 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).
STOR 853 - NONPARAMETRIC INFERENCE: SMOOTHING METHODS
Prerequisites: STOR 635 and 655. 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).
STOR 854 - STATISTICAL LARGE SAMPLE THEORY -
Prerequisites: STOR 635 and 655. Asymptotically efficient estimators; maximum likelihood estimators. Asymptotically optimal tests; likelihood ratio tests. (3).
STOR 855- SUBSAMPLING TECHNIQUES -
Prerequisite: STOR 655. 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).
STOR 831 - ADVANCED PROBABILITY -
Prerequisites: STOR 634 and 635. Advanced theoretical course covering topics selected from: weak convergence theory, central limit theorems, laws of large numbers, stable laws, random walks, martingales. Budhiraja, Pipiras, Leadbetter. (3).
STOR 832- STOCHASTIC PROCESSES -
Prerequisites: STOR 634 and 635. Advanced theoretic course including topics selected from: Foundations of stochastic processes, renewal processes, stationary processes, Markov processes, martingales, point processes. Budhiraja, Pipiras, Leadbetter (3).
STOR 833- TIME SERIES ANALYSIS -
Prerequisites: STOR 754. 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, Smith. (3).
STOR 834 - EXTREME VALUE THEORY -
Prerequisites: STOR 634 and 635. 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).
STOR 835- POINT PROCESSES -
Prerequisite: STOR 635. 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).
STOR 836- STOCHASTIC ANALYSIS -
Prerequisite: STOR 634 and 635, 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. Budhiraja (3).
STOR 856- MULTIVARIATE ANALYSIS -
Prerequisites: STOR 655 and matrix theory. 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. Sen (3).
STOR 857- NONPARAMETRIC MULTIVARIATE ANALYSIS -
Prerequisite: STOR 852. 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).
STOR 940, 960- SEMINAR IN THEORETICAL STATISTICS -
Prerequisite: STOR 655. (3).
STOR 890, 891- SPECIAL PROBLEMS -
Prerequisite: permission of the instructor. (3).
STOR 930, STAT 950- ADVANCED RESEARCH -
Prerequisite: permission of the instructor. (3).
STOR 970 - Practicum
Students work with other organizations (Industrial/Governmental) to gain practiced experience in Statistics and Operations Research. Students prepare a report based on their experience. (1-15).
STOR 992- MASTER'S ESSAY -
Prerequisite, permission of the student's adviser. Fall and Spring. Staff. A minimum of 3 credit hours of 992 is required for the M.S. degree.
STOR 994- DOCTORAL DISSERTATION -
Prerequisite, permission of the student's adviser. Fall and spring. Staff. A minimum of 6 credit hours of 694 is required for the PhD degree.
