# Statistics Course Descriptions

**Undergraduate Courses
**

**STOR 151 INTRODUCTION TO DATA ANALYSIS (3)**

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. Fall, Spring, Summer. Staff.

**STOR 155 INTRODUCTION TO DATA MODELS AND INFERENCE (3)**

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. Fall, Spring. Staff.

**STOR 435 INTRODUCTION TO PROBABILITY (MATH 535)** **(3)**

Prerequisites: 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, Spring, Summer. Bhamidi, Ji, Kulkarni, Pipiras.

**STOR 455 STATISTICAL METHODS I (3)**

Prerequisite: STOR 155 or equivalent. Review of basic inference; two-sample comparisons; correlation; introduction to matrices; simple and multiple regression (including significance tests, diagnostics, variable selection); analysis of variance; use of statistical software.Fall, Spring, Summer. Cunningham, Sen, Zhang.

**STOR 555 MATHEMATICAL STATISTICS** **(3)**

Prerequisite: STOR 435 or equivalent. Functions of random samples and their probability distributions, introductory theory of point and interval estimation and hypothesis testing, elementary decision theory. Fall. Carlstein.

**STOR 556 ADVANCED METHODS OF DATA ANALYSIS (3)**

Prerequisite: STOR 435 and STOR 455. Topics selected from: design of experiments, sample surveys, nonparametrics, time-series, multivariate analysis, contingency tables, logistic regression, and simulation. Use of statistical software packages. Spring. Zhang.

**STOR 565 MACHINE LEARNING (3)**

Prerequisites, STOR 215 or MATH 381, and STOR 435. Introduction to theory and methods of machine learning including classification; Bayes risk/rule, linear discriminant analysis, logistic regression, nearest neighbors, and support vector machines; clustering algorithms; overfitting, estimation error, cross validation. Spring. Nobel.

**Graduate Courses**

**STOR 634 PROBABILITY I** **(3)**

Prerequisite: advanced calculus. Lebesgue and abstract measure and integration, convergence theorems, differentiation. Radon-Nikodym theorem, product measures. Fubini theorems. Lp spaces. Fall. Bhamidi, Fraiman.

**STOR 635 PROBABILITY II (3)**

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. Bhamidi, Budhiraja.

**STOR 641 STOCHASTIC MODELS IN OPERATIONS RESEARCH I (3)**

Prerequisites: STOR 435. Review of probability, conditional probability, expectations, transforms, generating functions, special distributions, and functions of random variables. Introduction to stochastic processes. Discrete-time Markov chains. Transient and limiting behavior. First passage times. Fall. Kulkarni, Ziya.

**STOR 654 STATISTICAL THEORY I (3)**

Prerequisite:two semesters of advanced calculus. Probability spaces. Random variables, distributions, expectation. Conditioning. Generating functions. Limit theorems: LLN, CLT, Slutsky, delta-method, big-O in probability. Inequalities. Distribution theory: normal, chi-squared, beta, gamma, Cauchy, other multivariate distributions. Distribution theory for linear models. Fall. Hannig, Ji.

**STOR 655 STATISTICAL THEORY II (3)**

Prerequisite: STOR 654.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. Spring. Hannig, Nobel. (3)

**STOR 664 APPLIED STATISTICS I (3)**

Prerequisite: STOR 555 or 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. Liu, Ji.

**STOR 665 APPLIED STATISTICS II (3)**

Prerequisite: STOR 664 or permission of the instructor. Analysis of variance (ANOVA), including nested and crossed models, and 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. Zhang**.
**

**STOR 754 TIME SERIES AND MULTIVARIATE ANALYSIS (3)**

Prerequisite: STOR 435 and 555. Introduction to time series: exploratory analysis, time-domain analysis and ARMA models, Fourier analysis, state space analysis. Introduction to multivariate analysis: principal components, canonical correlation, classification and clustering, dimension reduction. Spring. Pipiras.

**STOR 755 ESTIMATION, HYPOTHESIS TESTING, AND STATISTICAL DECISION (3)**

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. Nobel.

**STOR 756 DESIGN AND ROBUSTNESS (3)**

Prerequisite, STOR 555. Introduction to experimental design, including classical designs, industrial designs, optimality, and sequential designs. Introduction to robust statistical methods; bootstrap, cross-validation, and resampling.

**STOR 757 BAYESIAN STATISTICS AND GENERALIZED LINEAR MODELS (3)**

Prerequisite, STOR 555. Bayes factors, empirical Bayes theory, applications of generalized linear models. Hannig.

**STOR 765 CONSULTING (3)**

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. (3 credits for one year)

**STOR 890, 891 SPECIAL PROBLEMS (1-3)**

Prerequisite: permission of the instructor.

**STOR 930, 950 ADVANCED RESEARCH (1-3)**

Prerequisite: permission of the instructor.

**STOR 940, 960 SEMINAR IN THEORETICAL STATISTICS (1-3)**

Prerequisite: STOR 655.

**STOR 970 Practicum (1-3)**

Students work with other organizations (Industrial/Governmental) to gain practiced experience in Statistics and Operations Research. Students prepare a report based on their experience.

**STOR 992 MASTER’S ESSAY (3)**

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 (3)**

Prerequisite, permission of the student’s adviser. Fall and spring. Staff. A minimum of 6 credit hours of 994 is required for the PhD degree.

**Advanced Graduate Courses
**

These courses are offered periodically, according to demand.

**STOR 831 ADVANCED PROBABILITY (3)**

Prerequisites: STOR 634 and 635.Advanced theoretic course, covering topics selected from weak convergence theory, central limit theorems, laws of large numbers, stable laws, infinitely divisible laws, random walks, martingales.

**STOR 832 STOCHASTIC PROCESSES (3)**

Prerequisites, STOR 634 and 635. Advanced theoretic course including topics selected from foundations of stochastic processes, renewal processes, Markov processes, martingales, point processes.

**STOR 833 TIME SERIES ANALYSIS (3)**

Prerequisites, STOR 634 and 635. 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.

**STOR 834 EXTREME VALUE THEORY (3)**

Prerequisites, STOR 635 and 654. Classical asymptotic distributional theory for maxima and order statistics from i.i.d. sequences, including extremal types theorem, domains of attraction, Poisson properties of high level exceedances. Stationary stochastic sequences and continuous time processes.

**STOR 835 POINT PROCESSES (3)**

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.

**STOR 836 STOCHASTIC ANALYSIS (3)**

Prerequisites, STOR 634 and 635. Brownian motion, semimartingale theory, stochastic integrals, stochastic differential equations, diffusions, Girsanov’s theorem, connections with elliptic PDE, Feynman-Kac formula. Applications: mathematical finance, stochastic networks, biological modeling.

**STOR 851 SEQUENTIAL ANALYSIS (3)**

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.

**STOR 852 NONPARAMETRIC INFERENCE: RANK-BASED METHODS (3)**

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.

**STOR 853 NONPARAMETRIC INFERENCE: SMOOTHING METHODS (3)**

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.

**STOR 854 STATISTICAL LARGE SAMPLE THEORY (3)**

Prerequisites: STOR 635 and 655. Asymptotically efficient estimators; maximum likelihood estimators. Asymptotically optimal tests; likelihood ratio tests.

**STOR 855 SUBSAMPLING TECHNIQUES (3)**

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.

**STOR 856 MULTIVARIATE ANALYSIS (3)**

Prerequisite, STOR 655. Required preparation, 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.

**STOR 857 NONPARAMETRIC MULTIVARIATE ANALYSIS (3)**

Prerequisite: STOR 852. Nonparametric MANOVA. Large sample properties of tests and estimates. Robust procedures in general linear models including growth curves. Nonparametric classification problems.

**STOR 881 OBJECT ORIENTED DATA ANALYSIS (3)**

Object Oriented Data Analysis (OODA) is the statistical analysis of populations of complex objects. Examples include data sets where the data points could be curves, images, shapes, movies, or tree structured objects.