Department of Statistics and Operations Research

AMARJIT BUDHIRAJA,* Chair*

**Professors**

Amarjit Budhiraja (2) Probability, Stochastic Analysis, Stochastic Control

Edward Carlstein (3) Nonparametric Statistics, Resampling

Jan Hannig (23) Statistics, Fiducial Inference, Stochastic Processes

Douglas G. Kelly (5) Statistics, Evolutionary Game Theory

Vidyadhar G. Kulkarni (6) Stochastic Models of Queues, Telecommunication Systems, Warranties, Supply Chains

Malcolm Ross Leadbetter (7) Probability, Statistics, Extreme Value Theory

Yufeng Liu (8) Carolina Center for Genome Sciences. Statistical Machine Learning, Data Mining, Bioinformatics, Experimental Designs

James Stephen Marron (10) Amos Hawley Distinguished Professor. Object-Oriented Data Analysis, Visualization, Smoothing

Andrew Nobel (11) Machine Learning, Data Mining, Computational Genomics

Vladas Pipiras (13) Long-Range Dependence, Self-Similarity, Heavy-Tails, Fractional Calculus, Wavelets, Applications to Telecommunications

J. Scott Provan (14) Network Design, Linear and Combinatorial Optimization, Bioinformatics

Pranab Kumar Sen (15) Cary C. Boshamer Professor. Statistical Inference, Multivariate Analysis, Sequential Analysis, Clinical Trials, Environmetrics, Bioinformatics.

Richard L. Smith (17) Mark L. Reed Distinguished Professor and Director, Statistical and Applied Mathematical Sciences Institute. Extreme Value Theory, Environmental Statistics, Spatial Statistics

**Associate Professors**

Nilay Argon (1) Stochastic Models, Queueing Design and Control, Healthcare Operations, Simulation

Chuanshu Ji (4) Financial Econometrics, Computational Materials Science, Monte Carlo Methods

Gabor Pataki (12) Convex Programming, Convex Analysis, Integer Programming

Haipeng Shen (16) Functional Data Analysis, Time Series, Statistical Modeling of Customer Contact Centers

Serhan Ziya (20) Stochastic Models, Revenue Management, Service Operations

**Assistant Professors**

Shankar Bhamidi (24) (25) Networks: Mathematical Models and Applications, Probablistic Combinatorial Optimization

Shu Lu (9) Optimization, Variational Inequalities

Kai Zhang (26) Mathematical Statistics, High Dimensional Inference, Inference after Variable Selection, Large Deviation, Quantum Computing

Yin Xia, Mathematical Statistics, Multivariate Analysis, High Dimensional Inference, Nonparametric Function Estimation

**Lecturers**

Robin Cunningham, Actuarial Models

Charles Dunn, Actuarial Models

Joint Professors

Jason Fine, Biostatistics, Nonparametrics

Joseph Ibrahim, Alumni Distinguished Professor of Biostatistics. Bayesian Methods, Missing Data, Cancer Research

Alan F. Karr, Director, National Institute of Statistical Sciences. Inference for Stochastic Processes, Image Analysis, Engineering Applications of Statistics

Michael Kosorok, Biostatistics, Biostatistics, Empirical Processes, Semiparametric Inference, Machine Learning, Personalized Medicine, Clinical Trials, Dynamic Treatment Regimes

Jayashankar Swaminathan, Benjamin Cone Research Professor, Kenan–Flagler Business School. Supply Chain, Stochastic Models

**Adjunct Professors**

Kenneth A. Bollen, H.R. Immerwahr Distinguished Professor of Sociology. Comparative Political Structures, Statistics, International Development

Harry L. Hurd, Stochastic Processes, Statistical Inference

Robert Rodriguez, Statistical Quality Improvement, Statistical Graphics

**Professors Emeriti**

Charles R. Baker

George S. Fishman

Douglas G. Kelly

J. Scott Provan

David S. Rubin

Gordon D. Simons

Walter L. Smith

Shaler Stidham Jr.

Jon W. Tolle

Graduate Degrees in Statistics and Operations Research

The department offers the master of science (M.S.) and doctor of philosophy (Ph.D.) in statistics and operations research (STOR). Each degree encompasses three programs: statistics (STAT), operations research (OR), and interdisciplinary statistics and operations research (INSTORE).

The Ph.D. degree in STOR is designed for students planning a career in teaching or research. This degree requires at least three (but usually four to five) years of full-time graduate study, predicated upon substantial undergraduate mathematical preparation. Research is a central component in the work of doctoral candidates. Research training consists of required core course work as well as electives that are designed to bring students up to date in their research field, and intensive one-on-one work with a faculty member on a specific dissertation topic. Doctoral students who want to pursue academic careers are provided with ample opportunities to teach introductory undergraduate courses, and they are given extensive training to develop their instructional skills. Doctoral students may also participate in paid internships with local industrial employers to gain experience in a business environment. Their professional skills are further enhanced by work on real-world projects with clients in the department's consulting courses. Several courses provide opportunities for students to give technical presentations and refine their communication skills.

The M.S. degree in STOR prepares students for jobs in industry and government, and for further graduate study. The philosophy of the M.S. degree is to train students in the basic theory and applications of statistics and/or operations research. Completion of the M.S. degree typically requires two years of full-time graduate study.

Further information on the graduate degree programs can be obtained from the department's home page on the Web at www.stat-or.unc.edu. Information about the OR, STAT, and INSTORE programs may also be obtained from the admissions chair of the individual programs, CB# 3260, Hanes Hall, The University of North Carolina at Chapel Hill, Chapel Hill, NC 27599.

Application forms for admission and/or financial aid are available through the Web site of The Graduate School at gradschool.unc.edu/admissions. Students can indicate on this application form whether they intend to pursue the degree program in OR, STAT, or INSTORE. Applicants are required to submit scores for both the Aptitude and Advanced Mathematics portions of the Graduate Record Examination (GRE) in support of their application, and a supplementary sheet providing brief course descriptions (including textbook title where applicable) of previous undergraduate and graduate courses in mathematics, probability, and statistics.

Graduate Program in Operations Research

Operations research is concerned with the process of decision-making for the purpose of optimal resource allocation. The spectrum of related activities includes basic research in optimization theory, development of deterministic and stochastic mathematical models as aids for decision-making and application of these models to real world problems. The principal steps in modeling consist of analyzing relationships that determine the probable future consequences of decision choices, and then devising appropriate measures of effectiveness in order to evaluate the relative merits of alternative actions. During the past 50 years, operations research has developed as a mathematical science whose methods of analysis are regularly employed in many diverse industries and governmental agencies.

The operations research faculty consists of a resident faculty and an interdisciplinary faculty, with programs of study that offer considerable opportunity for the pursuit of individual student interests. Specialization is possible in deterministic optimization theory (such as nonlinear and integer programming), in stochastic processes and applied probability (such as queueing theory and simulation) or in an approved area of application (such as management science). The M.S. program is intended for the student who is preparing for a career in industry, government, or consulting. The Ph.D. program emphasizes theoretical depth and is tailored primarily for the student who is preparing for a career in teaching and/or research. Each program includes study of the mathematical foundations of operations research. In either case, the specific program of study for each student is determined to a large extent on an individual basis through consultations with a faculty advisor to obtain a balance between application and theory. Although it is possible for the well-prepared student to complete the M.S. requirements in three semesters, it more typically requires four semesters. The Ph.D. program, including the dissertation, generally requires four or five years beyond the bachelor's degree. The department offers a minor for Ph.D. students in other departments. The department also offers a course sequence that enables qualified UNC–Chapel Hill undergraduates in the mathematical decision sciences B.S. degree program to fulfill the requirements for the M.S. degree in operations research in one additional academic year (beyond the four years required for the undergraduate degree).

Requirements for Admission to Graduate Study in Operations Research

Applicants must have demonstrated a high level of scholastic ability in their undergraduate studies and must satisfy the entrance requirements of The Graduate School. No restrictions are placed on the undergraduate major for admission to the program. However, to be prepared adequately for study in operations research, an applicant should have a good mathematical background, including courses in advanced calculus, linear or matrix algebra, probability and statistics, and the knowledge of a computer language. A student admitted with a deficiency in one or more of these topics must make up for it at the beginning of her or his graduate work. If the deficiency is not severe, this can be accomplished without interrupting the normal program.

Degree Requirements for Operations Research

Candidates for degrees in operations research must meet the general requirements of The Graduate School. Course selections for a degree in operations research are taken from the department's offerings and from the regular offerings of related departments including Biostatistics, City and Regional Planning, Computer Science, Epidemiology, Economics, Health Policy and Management, Information and Library Science, Mathematics, Psychology, the Kenan–Flagler Business School, and the Fuqua School of Business at Duke University.

For more details, see stat-or.unc.edu/programs and click on "Operations Research."

Graduate Program in Statistics

The statistics program offers graduate training leading to the master of science (M.S.) and doctor of philosophy (Ph.D.) degrees. The M.S. degree may be included in the doctoral program.

**M.S. Program**

The statistics M.S. program provides students with rigorous training in one or more areas of statistics and probability. The program is flexible enough to accommodate students with a variety of backgrounds and a variety of career interests.

The M.S. degree provides a valuable complement to a number of Ph.D. programs in the sciences and social sciences, and enhances the credentials of students in these programs seeking academic or industrial jobs. Over the years, students have completed the statistics M.S. degree concurrently with a Ph.D. in other areas such as economics, sociology, psychology, mathematics, and physics.

The statistics M.S. degree requires 30 credit hours of course work and the completion of a master's project. Students can choose from a wide variety of courses, including a limited number from outside the department. Upon approval of The Graduate School, at most six credit hours may be transferred from another accredited institution, or from within UNC–Chapel Hill for courses taken before admission to the M.S. program.

**Ph.D. Program**

The Ph.D. program in statistics provides students with a broad-based course of study in applied statistics, theoretical statistics and probability, as well as numerous advanced topic courses. The breadth and depth of the program has served graduates well in their subsequent careers in academia, industry, and government. Doctoral students pursue a wide range of dissertation research topics ranging from applied statistics to theoretical probability. Many students are involved in interdisciplinary research that puts them in regular contact with faculty and students from other disciplines.

Basic Requirements for the Statistics Ph.D.

The Ph.D. degree requires at least 45 semester hours of graduate course work and the successful completion of a doctoral dissertation. To meet the course requirements, students typically take 15 three-credit courses. Most courses are selected from among those offered by the statistics program, but approved courses from outside the program can also be counted toward the 45-credit minimum.

The Ph.D. curriculum in statistics places strong emphasis on the mathematical foundations of statistics and probability. A sound mathematical preparation is thus an essential prerequisite for admission to the program. An applicant's mathematical background should include a one-year course in real analysis, at least one semester of matrix algebra, and calculus-based courses in probability and statistics.

For more details, see stat-or.unc.edu/programs/statistics/phd.

Applicants for financial aid are considered for assistantships within the department, as well as for various fellowships and limited service awards provided on a competitive University-wide basis by The Graduate School. Assistants perform academically related duties, such as teaching, grading, and leading tutorials. Other awards include merit assistantships, University graduate and alumni fellowships, Pogue fellowships, and Morehead fellowships. Assistantships and fellowships generally include a stipend for the academic year as well as tuition.

Application for admission and financial aid may be made simultaneously simply by indicating on the admission application form a desire to be considered for financial aid.

More detailed information about the statistics program is available on the department's home page (listed above). Specific inquiries should be addressed to the Director of Graduate Admissions, Statistics Program, CB# 3260, The University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-3260.

Statistics Courses for Students from Other Disciplines

A number of STOR courses in probability and statistics are of potential interest to students in other disciplines. At the advanced undergraduate/beginning graduate level, STOR 455 and 456 provide an introduction to applied statistics, including regression, analysis of variance, and time series. STOR 435 and 555 provide introductions to probability theory and mathematical statistics, respectively, at a post-calculus level.

The three graduate course sequences–(664, 665), (654, 655), and (634, 635)–provide comprehensive introductions to modern applied statistics, theoretical statistics, and probability theory, respectively, at a more mathematical level. In each case it is possible to take only the first course in the sequence. Concerning mathematical prerequisites, 664 and 665 require a background in linear algebra and matrix theory, while the remaining courses require a solid background in real-analysis.

INSTORE Program

A Ph.D. and M.S. program entitled Interdisciplinary Statistics and Operations Research (INSTORE) was established in the fall semester of 2007. The INSTORE program is suitable for students pursuing an interdisciplinary research agenda who want to combine elements from the traditional statistics and operations research programs, or who want to develop significant expertise in the applications of statistics and operations research to some outside area such as genetics, finance, social science, or environmental science. The INSTORE program allows flexibility for adaptively combining statistics, operations research, and external fields of application. However, there are specific tracks that contain suggested sequences of courses allowing students to focus on certain areas of study. For example, there is a track in applied statistics and optimization, a track in computational finance, and a track in business analytics; further tracks are planned in econometrics and in bioinformatics. A mechanism also exists for students to propose their own track (subject to approval by the department's faculty). For detailed descriptions of the content and requirements of the INSTORE program go to stat-or.unc.edu/programs and click on "Interdisciplinary Statistics and Operations Research."

Courses for Graduate and Advanced Undergraduate Students

*STOR*

**415 Deterministic Models in Operations Research (3).** Prerequisite, MATH 547. Linear, integer, nonlinear, and dynamic programming, classical optimization problems, network theory.

**435 Introduction to Probability (MATH 535) (3).** Prerequisite, MATH 233. Introduction to the 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.

**445 Stochastic Models in Operations Research (3).** Prerequisite, BIOS 660 or STOR 435. Introduction to Markov chains, Poisson processes, continuous-time Markov chains, renewal theory. Applications to queueing systems, inventory, and reliability, with emphasis on systems modeling, design, and control.

**455 Statistical Methods I (3).** Prerequisite, STOR 155. 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.

**465 Simulation Analysis and Design (3).** Prerequisite, STOR 445. Introduces concepts of random number generation, random variate generation, and discrete event simulation of stochastic systems. Students perform simulation experiments using standard simulation software.

**471 Long-Term Actuarial Models (3).** Prerequisite, STOR 435. Probability models for long-term insurance and pension systems that involve future contingent payments and failure-time random variables. Introduction to survival distributions and measures of interest and annuities-certain.

**472 Short Term Actuarial Models (3).** Prerequisite, STOR 435. Short-term probability models for potential losses and their applications to both traditional insurance systems and conventional business decisions. Introduction to stochastic process models of solvency requirements.

**493 Internship in Statistics and Operations Research (3).** Requires permission of the department. Mathematical decision sciences majors only. An opportunity to obtain credit for an internship related to statistics, operations research, or actuarial science. Pass/Fail only. Does not count toward the mathematical decision sciences major or minor.

**496 Undergraduate Reading and Research in Statistics and Operations Research (1–3).** Permission of the director of undergraduate studies. This course is intended mainly for students working on honors projects. May be repeated for credit.

**515 Computational Mathematics for Decision Sciences (3).** Permission of the instructor. Reviews basic mathematical and computational theory required for analyzing models that arise in operations research, management science, and other policy sciences. Solution techniques that integrate existing software into student-written computer programs will be emphasized.

**555 Mathematical Statistics (3).** Prerequisite, STOR 435. Functions of random samples and their probability distributions, introductory theory of point and interval estimation and hypothesis testing, elementary decision theory.

**556 Statistical Methods II (3).** Prerequisite, STOR 435 and 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.

**565 Introduction to 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.

**582 Neural Network Models for the Decision and Cognitive Sciences (3).** Prerequisite, MATH 231, PHIL 155, PSYC 210, or STOR 155 or 215. The interactions between cognitive science and the decision sciences are explored via neural networks. The history of these networks in neuroscience is reviewed and their adaptation to other fields such as psychology, linguistics, and operations research is presented.

**612 Models in Operations Research (3).** Required preparation, calculus of several variables, linear or matrix algebra. Formulation, solution techniques, and sensitivity analysis for optimization problems which can be modeled as linear, integer, network flow, and dynamic programs. Use of software packages to solve linear, integer, and network problems.

**614 Linear Programming (3).** Required preparation, calculus of several variables, linear or matrix algebra. The theory of linear programming, computational methods for solving linear programs, and an introduction to nonlinear and integer programming. Basic optimality conditions, convexity, duality, sensitivity analysis, cutting planes, and Karush-Kuhn-Tucker conditions.

**634 Measure and Integration (3).** Required preparation, advanced calculus. Lebesgue and abstract measure and integration, convergence theorems, differentiation. Radon-Nikodym theorem, product measures. Fubini theorems. Lp spaces.

**635 Probability (MATH 635) (3).** Prerequisite, STOR 634. Permission of the instructor for students lacking the prerequisite. Foundations of probability. Basic classical theorems. Modes of probabilistic convergence. Central limit problem. Generating functions, characteristic functions. Conditional probability and expectation.

**641 Stochastic Models in Operations Research I (3).** Prerequisite, 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.

**642 Stochastic Models in Operations Research II (3).** Prerequisite, STOR 641. Exponential distribution and Poisson process. Birth-death processes, continuous-time Markov chains. Transient and limiting behavior. Applications to elementary queueing theory. Renewal processes and regenerative processes.

**654 Statistical Theory I (3).** Required preparation, 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.

**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.

**664 Applied Statistics I (3).** 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.

**665 Applied Statistics II (3).** Prerequisite, STOR 664. Permission of the instructor for students lacking the prerequisite. 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.

**691H Honors in Mathematical Decision Sciences (3).** Permission of the department. Majors only. Individual reading, study, or project supervised by a faculty member.

**692H Honors in Mathematical Decision Sciences (3).** Permission of the department. Majors only. Individual reading, study, or project supervised by a faculty member.

Courses for Graduate Students

**STOR**

**701 Statistics and Operations Research Colloquium (1).** This seminar course is intended to give Ph.D. students exposure to cutting edge research topics in statistics and operations research and assist them in their choice of a dissertation topic. The course also provides a forum for students to meet and learn from major researchers in the field.

**705 Operations Research Practice (3).** Prerequisites, STOR 614, 641, and 762. Permission of the instructor. Gives students an opportunity to work on an actual operations research project from start to finish under the supervision of a faculty member. Intended exclusively for operations research students.

**712 Mathematical Programming I (3).** Prerequisites, MATH 661 or STOR 515, and STOR 614. Permission of the instructor for students lacking the prerequisites. Advanced topics from mathematical programming such as geometry of optimization, parametric analysis, finiteness and convergence proofs, and techniques for large-scale and specially structured problems.

**713 Mathematical Programming II (3).** Prerequisite, STOR 712. Permission of the instructor for students lacking the prerequisite. Advanced theory for nonlinear optimization. Algorithms for unconstrained and constrained problems.

**722 Integer Programming (3).** Prerequisite, STOR 614. Permission of the instructor for students lacking the prerequisite. Techniques for formulating and solving discrete valued and combinatorial optimization problems. Topics include enumerative and cutting plane methods, Lagrangian relaxation, Benders' decomposition, knapsack problems and matching and covering problems.

**724 Networks (3).** Prerequisite, STOR 614. Permission of the instructor for students lacking the prerequisites. Network flow problems and solution algorithms; maximum flow, shortest route, assignment, and minimum cost flow problems; Hungarian and out-of-kilter algorithms; combinatorial and scheduling applications.

**734 Stochastic Processes (3).** Prerequisite, STOR 435. Discrete and continuous parameter Markov chains, Brownian motion, stationary processes.

**743 Stochastic Models in Operations Research III (3).** Prerequisite, STOR 642. Intermediate queueing theory, queueing networks. Reliability. Diffusion processes and applications. Markov decision processes (stochastic dynamic programming): finite horizon, infinite horizon, discounted and average-cost criteria.

**744 Queueing Networks (3).** Prerequisite, STOR 642. Permission of the instructor for students lacking the prerequisite. Jackson networks; open and closed. Reversibility and quasi-reversibility. Product form networks. Nonproduct form networks. Approximations. Applications to computer performance evaluations and telecommunication networks.

**754 Time Series and Multivariate Analysis (3).** Prerequisites, 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.

**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.

**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.

**757 Bayesian Statistics and Generalized Linear Models (3).** Prerequisite, STOR 555. Bayes factors, empirical Bayes theory, applications of generalized linear models.

**762 Discrete Event Simulation (COMP 762) (3).** Prerequisites, STOR 555 and 641. Familiarity with computer programming required. Introduces students to modeling, programming and statistical concepts applicable to discrete event simulation on digital computers. Emphasizes statistical analysis of simulation output. Students model, program, and run simulations.

**763 Statistical Quality Improvement (3).** Prerequisites, STOR 655 and 664. Methods for quality improvement through process control, graphical methods, designed experimentation. Shewhart charts, cusum schemes, methods for autocorrelated multivariate process data, process capability analysis, factorial and response surface designs, attribute sampling.

**765 Statistical Consulting (3).** Application of statistics to real problems presented by researchers from the University and local companies and institutes. (Taught over two semesters.)

**767 Advanced Statistical Machine Learning (3).** Prerequisites, STOR 654,655, 664, 665 and permission of the instructor. This is a graduate course on statistical machine learning.

**772 Introduction to Inventory Theory (3).** Permission of the instructor. Introduction to the techniques of constructing and analyzing mathematical models of inventory systems.

**790 Operations Research and Systems Analysis Student Seminar (1).** Survey of literature in operations research and systems analysis.

**822 Topics in Discrete Optimization (COMP 822) (3).** Prerequisite, STOR 712. Permission of the instructor. Topics may include polynomial algorithms, computational complexity, matching and matroid problems, and the traveling salesman problem.

**824 Computational Methods in Mathematical Programming (3).** Prerequisites, STOR 712. Permission of the instructor. Advanced topics such as interior point methods, parallel algorithms, branch and cut methods, and subgradient optimization.

**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.

**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.

**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.

**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.

**835 Point Processes (3).** Prerequisite, STOR 635. Random measures and point processes on general spaces, Poisson and related processes, regularity, compounding. Point processes on the real line stationarity, Palm distributions, Palm-Khintchine formulae. Convergence and related topics.

**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.

**842 Control of Stochastic Systems in Operations Research (3).** Prerequisites, STOR 641 and 642. Review of Markov decision processes. Monotone control policies. Algorithms. Examples: control of admission, service, routing and scheduling in queues and networks of queues. Applications: manufacturing systems, computer/communication systems.

**851 Sequential Analysis (3).** Prerequisites, STOR 635 and 655. Hypothesis testing and estimation when sample size depends on the observations. Sequential probability ratio tests. Sequential design of experiments. Optimal stopping. Stochastic approximation.

**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.

**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.

**854 Statistical Large Sample Theory (3).** Prerequisites, STOR 635 and 655. Asymptotically efficient estimators; maximum likelihood estimators. Asymptotically optimal tests; likelihood ratio tests.

**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.

**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.

**857 Nonparametric Multivariate Analysis (3).** 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.

**890 Special Problems (1–3).** Permission of the instructor.

**891 Special Problems (1–3).** Permission of the instructor.

**892 Special Topics in Operations Research and Systems Analysis (1–3).** Permission of the instructor.

**893 Special Topics (1–3).** Advance topics in current research in statistics and operations research.

**910 Directed Reading in Operations Research and Systems Analysis (1–21).** Permission of the instructor.

**930 Advanced Research (1-3).** Permission of the instructor

**950 Advanced Research (0.5–21).** Permission of the instructor.

**940 Seminar in Theoretical Statistics (1-3).** Prerequisite, STOR 655.

**960 Seminar in Theoretical Statistics (0.5–21).** Prerequisite, STOR 655.

**970 Practicum (1–3).** Students work with other organizations (Industrial/Governmental) to gain practiced experience in Statistics and Operations Research.

**992 Master's (Non-Thesis) (3).** Permission of instructor.

**994 Doctoral Research and Dissertation (3).** Permission of instructor.