Department of Statistics and Operations Research
VIDYADHAR KULKARNI, Chair
Professors
Amarjit Budhiraja (2) Probability, Stochastic Analysis, Stochastic Control
Edward Carlstein (3) Nonparametric Statistics, Resampling
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
James Stephen Marron, Amos Hawley Distinguished Professor (10) Object Oriented Data Analysis, Visualization, Smoothing
Andrew Nobel (11) Machine Learning, Data Mining, Computational Genomics
J. Scott Provan (14) Network Design, Linear and Combinatorial Optimization, Bio-informatics
Richard L. Smith, Mark L. Reed Distinguished Professor (17) Extreme Value Theory, Environmental Statistics, Spatial Statistics
Jon W. Tolle (18) Optimization
Associate Professors
Jan Hannig (23) Statistics, Fiducial Inference, Stochastic Processes
Chuanshu Ji (4) Financial Econometrics, Computational Materials Science, Monte Carlo Methods
Gabor Pataki (12) Convex Programming, Combinatorial Optimization, Integer Programming
Vladas Pipiras (13) Long-Range Dependence, Self-Similarity, Heavy-Tails, Fractional Calculus, Wavelets, Applications to Telecommunications
Assistant Professors
Nilay Argon (1) Stochastic Models, Manufacturing and Health Care Applications, Simulation
Yufeng Liu, Carolina Center for Genome Sciences (8) Statistical Machine Learning, Data Mining, Bioinformatics, Experimental Designs
Shu Lu (9) Optimization, Variational Inequalities
Haipeng Shen (16) Functional Data Analysis, Time Series, Statistical Modeling of Customer Contact Centers
Zhengyuan Zhu (19) Spatial Statistics, Spatial Sampling Design, Anomaly Detection
Serhan Ziya (20) Stochastic Models, Revenue Management, Service Operations
Lecturer
Charles Dunn, Actuarial Models
Joint Professors
Alan F. Karr, Director, National Institute of Statistical Sciences, Inference for Stochastic Processes, Image Analysis, Engineering Application of Statistics
Michael Kosorok, Biostatistics
Pranab Kumar Sen, Cary C. Boshamer Professor of Biostatistics (15) Nonparametric Methods, Multivariate Analysis, Sequential Analysis
Jayashankar Swaminathan, Benjamin Cone Research Professor, Kenan–Flagler Business School, Supply Chain, Stochastic Models
Adjunct Professors
Kenneth A. Bollen, Comparative Political Structures, Statistics, International Development
George Christakos, Environmental Sciences and Engineering
Mark E. Hartmann, Combinatorial Optimization, Integer Programming, Polyhedral Combinatorics
Harry L. Hurd, Stochastic Processes, Statistical Inference
Eric Renault, Econometrics, Finance
Robert Rodriguez, Statistical Quality Improvement, Statistical Graphics
Randy Tobias, Linear Models, Experimental Design
Harvey M. Wagner (22) Management, Strategic Thinking, Modeling
Professors Emeriti
Charles R. Baker
George S. Fishman
Gopinath Kallianpur, Alumni Distinguished Professor Emeritus
David S. Rubin
Gordon D. Simons
Walter L. Smith
Shaler Stidham Jr.
Graduate Degrees in Statistics and Operations Research
Since the fall semester of 2007, the department has offered the master of science (M.S.) and doctor of philosophy (Ph.D.) in statistics and operations research (STOR). Within each degree, the department runs 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. The training for research consists of required core course work as well as electives that are designed to bring students up to date in their research field, followed by 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 working on real-world projects with clients in the department's consulting courses. Several courses provide opportunities for students to give technical presentations and to 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 operations research. In addition to their course work, M.S. students also complete a master's essay under the supervision of a faculty member. Opportunities for teaching, consulting and internships are also available to M.S. students. 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 or INSTORE programs may also be obtained from the admissions chair of the individual programs, CB# 3260, Smith Building, The University of North Carolina at Chapel Hill, Chapel Hill, N.C. 27599.
Application forms for admission and/or financial aid may be obtained by writing to either The Graduate School or to the department. An online application is also available through the Web site of The Graduate School at gradschool.unc.edu. Students can indicate on this application form whether they intend to pursue the degree program in OR 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 text title where applicable) or 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 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 regular offerings of related departments. In addition to the following courses, selections can be made from the departments of Biostatistics, City and Regional Planning, Computer Science, Epidemiology, Economics, Health Policy and Administration, Information and Library Science, Mathematics, Psychology, the Kenan–Flagler Business School and the Fuqua School of Business in Duke University.
For more details, see stat-or.unc.edu/programs and click on "Operations Research."
Courses for Graduates and Advanced Undergraduates
305 [140] DECISION MAKING USING SPREADSHEET MODELS (3). Prerequisite, STAT 155 or MATH 152. The use of mathematics to describe and analyze large-scale decision problems. Situations involving the allocation of resources, making decisions in a competitive environment and dealing with uncertainty are modeled and solved using suitable software packages. Fall.
372 [161] LONG TERM ACTUARIAL MODELS (3). Prerequisites, MATH 232 or 215, and STAT 155. 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. Fall. Dunn.
415 DETERMINISTIC MODELS IN OPERATIONS RESEARCH (3). Prerequisite, MATH 547. Linear, integer, nonlinear and dynamic programming, classical optimization problems, network theory. Fall. Provan, Tolle.
435 INTRODUCTION TO PROBABILITY (MATH 535) (3). 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.
445 STOCHASTIC MODELS IN OPERATIONS RESEARCH (3). Prerequisite, BIOS 660 or STOR 435. Introduction to Markov chains, Poisson process, continuous-time Markov chains, renewal theory. Applications to queueing systems inventory, and reliability, with emphasis on systems modeling, design and control. Spring. Kulkarni, Stidham.
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.
456 STATISTICAL METHODS II (3). 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.
465 SIMULATION ANALYSIS AND DESIGN (3). Prerequisite, STOR 435. Introduces concepts of random number generation, random variate generation, and discrete event simulation of stochastic systems. Students perform simulation experiments using standard simulation software.
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. Spring. Dunn.
497 UNDERGRADUATE READING AND RESEARCH IN OPERATIONS RESEARCH (3). Permission of the director of undergraduate studies. This course is intended mainly for students working on honors projects. No one may receive more than three semester hours credit for this course.
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. Fall.
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.
582 NEURAL NETWORK MODELS FOR THE DECISION AND COGNITIVE SCIENCES (3). Prerequisite, one of MATH 231, PHIL 155, PSYC 210, 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.
Courses for Graduates
612 [210] MODELS IN OPERATIONS RESEARCH (3). Prerequisite, calculus of several variables, linear or matrix algebra. Formulation, solution techniques and sensitivity analysis for optimization problems that can be modeled as linear, integer, network flow and dynamic programs. Use of software packages to solve linear, integer and network problems. Fall. Rubin, Wagner.
614 [211] LINEAR PROGRAMMING (3). Prerequisites, 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. Spring. Provan, Rubin.
634 [154] MEASURE AND INTEGRATION (3). Prerequisite, advanced calculus. Lebesgue and abstract measure and integration, convergence theorems, differentiation. Radon-Nikodym theorem, product measures. Fubini theorems. Lp spaces.
635 [155] PROBABILITY (MATH 635) (3). Prerequisite, STOR 634 or permission of the instructor. Foundations of probability. Basic classical theorems. Modes of probabilistic convergence. Central limit problem. Generating functions, characteristic functions. Conditional probability and expectation.
641 [220] STOCHASTIC MODELS IN OPERATIONS RESEARCH I (3). Prerequisite, STOR 435 or equivalent. Review of probability, conditional probability, expectations, transforms, generating functions, special distributions, functions of random variables. Introduction to stochastic processes. Discrete-time Markov chains. Transient and limiting behavior. First passage times. Fall. Tekin, Ziya.
642 [221] STOCHASTIC MODELS IN OPERATIONS RESEARCH II (3). Prerequisite, STOR 641 or equivalent. 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. Spring. Kulkarni, Ziya.
654 [164] STATISTICAL THEORY I (3). Prerequisite, two semesters of advanced calculus. Probability spaces. Random variables, distributions, expectation. Conditioning. Generating functions. Limit theorems: LLN, CLT, Slutzky, delta-method, big-O in probability. Inequalities. Distribution theory: normal, chi-squared, beta, gamma, Cauchy, other multivariate distributions. Distribution theory for linear models.
655 [165] STATISTICAL THEORY II (3). 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.
664 [174] 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 [175] APPLIED STATISTICS II (3). 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.
705 [350] OPERATIONS RESEARCH PRACTICE (3). Prerequisites, OR 614, 641, 762 and 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. Spring.
712 [212] MATHEMATICAL PROGRAMMING I (3). Prerequisites, OR 614 and either OR 515 or MATH 661 or permission of the instructor. 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. Spring. Tolle.
713 [213] MATHEMATICAL PROGRAMMING II (3). Prerequisite, OR 712 or permission of the instructor. Advanced theory for nonlinear optimization. Algorithms for unconstrained and constrained problems. Fall. (Alternate years.) Tolle.
722 [214] INTEGER PROGRAMMING (3). Prerequisite, OR 614 or permission of the instructor. 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. (Alternate years.) Rubin.
724 [215] NETWORKS (3). Prerequisite, OR 614 or permission of the instructor. 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. Spring. Provan.
743 [222] STOCHASTIC MODELS IN OPERATIONS RESEARCH III (3). Prerequisite, OR 642 or equivalent. 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. Fall. Tekin, Ziya.
744 [223] QUEUEING NETWORKS (3). Prerequisite, OR 642 or permission of the instructor. Jackson networks; open and closed. Reversibility and quasi-reversibility. Product form networks. Nonproduct form networks. Approximations. Applications to computer performance evaluations and telecommunication networks. (Alternate years.) Tekin, Ziya.
762 [233] DISCRETE EVENT SIMULATION (COMP 762) (3). Prerequisites, STAT 555 and OR 641, or the equivalent and familiarity with computer programming. 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. Fall. Tekin, Ziya.
772 [225] INTRODUCTION TO INVENTORY THEORY (3). Prerequisite, permission of the instructor. Introduction to the techniques of constructing and analyzing mathematical models of inventory systems. (On demand.) Wagner, Swaminathan.
790 [389] OPERATIONS RESEARCH AND SYSTEMS ANALYSIS STUDENT SEMINAR (1). Survey of literature in operations research and systems analysis. Spring. Staff.
822 [216] TOPICS IN DISCRETE OPTIMIZATION (COMP 822) (3). Prerequisites, OR 712 and permission of the instructor. Topics may include polynomial algorithms, computational complexity, matching and matroid problems, and the traveling salesman problem. (Alternate years.) Provan.
824 [217] COMPUTATIONAL METHODS IN MATHEMATICAL PROGRAMMING (3). Prerequisites, OR 712 and permission of the instructor. Advanced topics such as interior point methods, parallel algorithms, branch and cut methods, and subgradient optimization. (Alternate years.) Provan.
842 [224] CONTROL OF STOCHASTIC SYSTEMS IN OPERATIONS RESEARCH (3). Prerequisites, OR 641 and OR 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. (Alternate years.) Tekin, Ziya.
892 [351] SPECIAL TOPICS IN OPERATIONS RESEARCH AND SYSTEMS ANALYSIS (Var.). Prerequisite, permission of the instructor. Fall and spring. Staff.
910 [321] DIRECTED READING IN OPERATIONS RESEARCH AND SYSTEMS ANALYSIS (Var.). Prerequisite, permission of operations research faculty member. Fall and spring. Staff.
992 [392] MASTER'S SUBSTITUTE FOR THESIS (3–21). Prerequisite, permission of the student's advisor. Fall and spring.
993 [393] MASTER'S THESIS (3–6). Prerequisite, permission of the student's advisor. Fall. Staff.
994 [394] DOCTORAL DISSERTATION (3-9). Prerequisite, permission of the student's advisor. Fall and spring. Staff.
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 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 areas such as economics, sociology, psychology, mathematics and physics.
The statistics M.S. degree requires 30 credit hours of course work and the preparation of a master's essay, typically under the direction of a faculty member in the statistics program. Preparation of the master's essay can be counted toward three hours of the 30-credit-hour minimum. 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, 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, and 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 and assisting instructors. Other awards include merit assistantships, University Graduate and Alumni fellowships, George E. Nicholson Jr. fellowships, Pogue fellowships and Morehead fellowships. Stipends range from $14,700 to $17,000 for the academic year, with tuition included with fellowship awards.
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, N.C. 27599-3260.
Courses for Graduates and Advanced Undergraduates
358 [104] SAMPLE SURVEY METHODOLOGY (BIOS 664) (4). Prerequisite, STAT 355 or equivalent. Fundamental principles and methods associated with survey sampling, giving primary attention to as nonmathematical as possible a treatment of simple random sampling, stratified sampling and cluster sampling. Also, techniques of questionnaire design, the problems of nonresponse and sources of nonsampling errors. Practical experience in the applied aspects of sampling is provided by student participation in the design, execution and analysis of an actual survey. Spring. Kalsbeek.
435 [126] INTRODUCTION TO PROBABILITY (MATH 435) (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. Fall and spring. Budhiraja, Kelly, Nobel.
555 [127] MATHEMATICAL STATISTICS (3). Prerequisite, STAT 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. Spring. Carlstein, Kelly, Simons.
634 [154] MEASURE AND INTEGRATION (3). Prerequisite, advanced calculus. Lebesgue and abstract measure and integration, convergence theorems, differentiation, Radon-Nikodym theorem, product measures, Fubini theorems, Lp spaces. Fall. Budhiraja, Leadbetter, Pipiras.
635 [155] PROBABILITY (MATH 635) (3). Prerequisite, STAT 634 or permission of the instructor. Foundations of probability. Basic classical theorems. Modes of probabilistic convergence. Central limit problem. Generating functions, characteristic functions. Conditional probability and expectation. Spring. Kelly, Leadbetter, Nobel.
654 [164] STATISTICAL THEORY I (3). Prerequisite, advanced calculus. Fundamentals of probability and distribution theory necessary for statistical inference. Fall. Kelly, Nobel, Simons.
655 [165] STATISTICAL THEORY II (3). Prerequisite, STAT 654. Fundamentals of statistical inference: point estimation, hypothesis testing and confidence sets, introduction to nonparametric statistics, introduction to decision theory and Bayesian inference. Spring. Simons, Ji, Marron.
664 [174] APPLIED STATISTICS I (3). Prerequisite, STAT 555 or equivalent. Introduction to linear models and multiple regression; introduction to statistical computing; statistical data analysis and visualization. Fall. Smith, Marron.
665 [175] APPLIED STATISTICS II (3). Prerequisite, STAT 664. Analysis of variance, generalized linear models, introduction to simulation, topics in numerical analysis. Spring. Smith, Marron, Zhu.
734 [184] STOCHASTIC PROCESSES (3). Prerequisite, STAT 435 or equivalent. Discrete and continuous parameter Markov chains, Brownian motion, stationary processes. Fall, alternate years. Leadbetter, Nobel, Ji.
754 [185] TIME SERIES AND MULTIVARIATE ANALYSIS (3). Prerequisites, STAT 435 and 555 or equivalents. 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, alternate years. Leadbetter, Marron, Smith.
756 [194] DESIGN AND ROBUSTNESS (3). Prerequisite, STAT 555 or equivalent. Introduction to experimental design, including classical designs, industrial designs, optimality and sequential designs. Introduction to robust statistical methods; bootstrap, cross-validation, and resampling. Fall, alternate years. Marron.
757 [195] BAYESIAN STATISTICS AND GENERALIZED LINEAR MODELS (3). Prerequisite, STAT 555 or equivalent. Bayes factors, empirical Bayes theory, applications of generalized linear models. Spring. Staff.
765 [190] STATISTICAL CONSULTING (3). Application of statistics to real problems presented by researchers from the University and local companies and institutes. (Taught over two semesters.) Fall and spring. Marron, Smith.
Courses for Graduates
755 [220] ESTIMATION, HYPOTHESIS TESTING AND STATISTICAL DECISION (3). Prerequisites, STAT 635 and 655 or equivalents. 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. Staff.
763 [205] STATISTICAL QUALITY IMPROVEMENT (3). Prerequisites, STAT 655, 664 or equivalent. 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. Rodriguez.
831 [231] ADVANCED PROBABILITY (3). Prerequisites, STAT 634 and 635 or equivalents. 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. Staff.
832 [232] STOCHASTIC PROCESSES (3). Prerequisites, STAT 634 and 635 or equivalents. Advanced theoretic course including topics selected from foundations of stochastic processes, renewal processes, Markov processes, martingales, point processes. Staff.
833 [233] TIME SERIES ANALYSIS (3). Prerequisites, STAT 634 and 635 or equivalents. 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.
834 [234] EXTREME VALUE THEORY (3). Prerequisites, STAT 635 and 654 or equivalents. 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. Leadbetter.
835 [235] POINT PROCESSES (3). Prerequisite, STAT 635 or equivalent. 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. Leadbetter.
836 [236] STOCHASTIC ANALYSIS (3). Prerequisites, STAT 634 and 635 or equivalents, 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. Pipiras, Budhhiraja.
851 [221] SEQUENTIAL ANALYSIS (3). Prerequisites, STAT 635 and 655 or equivalents. Hypothesis testing and estimation when sample size depends on the observations. Sequential probability ratio tests. Sequential design of experiments. Optimal stopping. Stochastic approximation. Staff.
852 [222] NONPARAMETRIC INFERENCE: RANK-BASED METHODS (3). Prerequisites, STAT 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.
853 [223] NONPARAMETRIC INFERENCE: SMOOTHING METHODS (3). Prerequisites, STAT 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.
854 [224] STATISTICAL LARGE SAMPLE THEORY (3). Prerequisites, STAT 635 and 655 or equivalents. Asymptotically efficient estimators; maximum likelihood estimators. Asymptotically optimal tests; likelihood ratio tests. Staff.
855 [225] SUBSAMPLING TECHNIQUES (3). Prerequisite, STAT 655 or equivalent. 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.
856 [260] MULTIVARIATE ANALYSIS (3). Prerequisites, STAT 655 and Introduction to 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. Fall. Staff.
857 [262] NONPARAMETRIC MULTIVARIATE ANALYSIS (3). Prerequisite, STAT 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.
Advanced Graduate-Level Courses*
890, 891 [321, 322] SPECIAL PROBLEMS (1–21). Prerequisite, permission of the instructor.
930, 950 [331, 332] ADVANCED RESEARCH (0.5–21). Prerequisite, permission of the instructor.
940, 960 [310, 311] SEMINAR IN THEORETICAL STATISTICS (0.5–21). Prerequisite, STAT 655.
993 [392] MASTER'S PAPER (3–6). Prerequisite, permission of the student's advisor. Fall and spring. Staff.
994 [394] DOCTORAL DISSERTATION (3–9). Prerequisite, permission of the student's advisor. Fall and spring. Staff.
*These courses are new or have been offered in recent years. Some of these courses will be offered on a regular basis with a course number after approval from The Graduate School.
PATTERN RECOGNITION. Nobel.
DESIGN AND CODING. Staff.
TOPICS IN COMPUTATIONAL FINANCE. Ji.
STOCHASTIC FINANCE. Staff.
ENVIRONMENTAL STATISTICS. Smith.
DATA-ANALYTIC MODELINGS AND THEIR APPLICATIONS. Staff.
GIBBS RANDOM FIELDS AND CERTAIN STATISTICAL APPLICATIONS. Ji.
TOPICS IN WEAK CONVERGENCE, MARKOV PROCESSES, AND STOCHASTIC DIFFERENTIAL EQUATIONS. Staff.
FUNCTIONAL DATA ANALYSIS. Marron.
INDUSTRIAL EXPERIMENTATION AND CLINICAL TRIALS: DESIGN AND STATISTICAL ANALYSIS. Staff.
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 postcalculus 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 a 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 new Ph.D. and M.S. program entitled "Interdisciplinary Statistics and Operations Research" (INSTORE) was established in the fall semester of 2007. This program is designed for students who seek a more flexible program than the two traditional programs (in statistics and in operations research separately), which continue to run alongside the new INSTORE program. 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 structure of the INSTORE program allows a great deal of flexibility for adaptively combining statistics, operations research and external fields of application. However, there are certain 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, and further tracks are planned in Econometrics and Financial Mathematics 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."