VIDYADHAR KULKARNI, Chair
Amarjit Budhiraja (2) Probability and Stochastic Processes, Stochastic Control and Filtering, Large Deviations, Stochastic Networks
Edward Carlstein (25) Stochastic Processes, Nonparametric Inference
Alan F. Karr (30) [Director, National Institute of Statistical Sciences] Inference for Stochastic Processes, Image Analysis, Engineering Application of Statistics
Douglas G. Kelly (4) Probability, Combinatorics, Biological Applications
Vidyadhar G. Kulkarni (14) Stochastic Models of Queues, Telecommunication Systems, Warranties, Supply Chains
Malcolm Ross Leadbetter (7) Probability, Stochastic Processes
James Stephen Marron (24) [Amos Hawley Distinguished Professor] Nonparametric Inference, Asymptotic Theory
Andrew Nobel (1) Nonparametric Statistics, Pattern Recognition
J. Scott Provan (20) Networks, Computational Complexity, Combinatorial Optimization
David S. Rubin (3) [Professor, Kenan-Flagler Business School] Integer Programming, Networks
Pranab Kumar Sen (13) [Cary C. Boshamer Professor of Biostatistics] Nonparametric Methods, Multivariate Analysis, Sequential Analysis
Richard L. Smith (27) [Reed Distinguished Professor] Extreme Value Theory, Time Series, Statistical Inference, Environmental Statistics
Jayashankar Swaminathan (22) [Benjamin Cone Research Professor, Kenan-Flagler Business School] Supply Chain, Stochastic Models
Jon W. Tolle (6) Optimization Theory
Chuanshu Ji (26) Statistical Modeling and Computing in Materials Science, Image Analysis, Quantitative Finance
Yufeng Liu (18) [Carolina Center for Genome Sciences] Machine Learning, Design of Experiments, Bioinformatics
Gabor Pataki (21) Convex Programming, Combinatorial Optimization, Integer Programming
Vladas Pipiras (11) Long-Range Dependence, Self-Similarity, Heavy-Tails, Fractional Calculus, Wavelets, Applications to Telecommunications
Haipeng Shen (12) Call Center Analysis, Queueing, Internet Traffic
Zhengyuan Zhu (15) Spatial Sampling Designs, Space-Time Modeling, Network Traffic
Serhan Ziya (28) Stochastic Models, Pricing in Congestion Systems
Charles Dunn, Actuarial Models
Mihail R. Rosu, Introduction to Statistics
Robert J. Adler (5) Stochastic Processes, Random Fields
Joseph Babu, SAMSI-Astrostatistics
Kenneth A. Bollen, Comparative Political Structures, Statistics, International Development
George Christakos, Environmental Sciences and Engineering
Jianqing Fan (9) Nonparametric Functional Estimation, Statistical Inference
Ronald Gallant (29) Econometrics, Nonlinear Models, Non-Parametric Inference
Mark E. Hartmann, Combinatorial Optimization, Integer Programming, Polyhedral Combinatorics
Harry L. Hurd, Stochastic Processes, Statistical Inference
Valen Johnson, Image Analysis, Bayesian Statistics, Binary Data
Vijay Marathe, Decision Models for Business
Randy Martens, Introduction to Decision Sciences
Suheil Nassar, NISS/IBM
Karl Petersen, Ergodic Theory
Eric Renault, Econometrics, Finance
Sidney Resnick, Risk Management
Robert Rodriguez, Statistical Quality Improvement, Statistical Graphics
David S. Rubin (3) [Professor, Kenan-Flagler Business School] Integer Programming, Networks
Pranab Kumar Sen (13) [Cary C. Boshamer Professor of Biostatistics] Nonparametric Methods, Multivariate Analysis, Sequential Analysis
Jayashankar Swaminathan (22) [Benjamin Cone Research Professor, Kenan-Flagler Business School] Supply Chain, Stochastic Models
Randy Tobias, Linear Models, Experimental Design
Harvey M. Wagner (19) Management, Strategic Thinking, Modeling
Charles R. Baker
George S. Fishman
Norman L. Johnson (Alumni Distinguished Professor Emeritus)
Gopinath Kallianpur (Alumni Distinguished Professor Emeritus)
Gordon D. Simons
Walter L. Smith
Shaler Stidham Jr.
The Department of Statistics and the Department of Operations Research were merged on July 1, 2003 to create the Department of Statistics and Operations Research. The merged department offers separate graduate programs in Operations Research and Statistics leading to MS and PhD degrees in Operations Research, and MS and PhD degrees in Statistics. It also offers an undergraduate degree program leading to a BS in Mathematical Decision Sciences. The graduate programs are listed separately below.
Further information on either program can be obtained from the department's home page on the Web at www.stat-or.unc.edu. Information about Operations Research may also be obtained from the Admissions Chair, Operations Research Program, CB# 3260, Smith Building, The University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, or by e-mailing stat-or@unc.edu. More information about the Statistics program may also be obtained from the Director of Graduate Admissions, Statistics Program, CB# 3260, The University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-3260.
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 fifty 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. Both the MS and PhD degrees are offered, with specialization 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 MS program is intended for the student who is preparing for a career in industry, government, or consulting. The PhD 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 adviser to obtain a balance between application and theory. Although it is possible for the well-prepared student to complete the MS requirements in three semesters, it more typically requires four semesters. The PhD program, including the dissertation, generally requires four or five years beyond the bachelor's degree. The department offers a minor for PhD students in other departments. The department also offers a course sequence that enables qualified UNC-Chapel Hill undergraduates in the mathematical decision sciences BS degree program to fulfill the requirements for the MS degree in operations research in one additional academic year (beyond the four years required for the undergraduate degree).
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.
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, and the Kenan-Flagler Business School.
Further information can be obtained from the department's home page (listed above), or from the Admissions Chair, Operations Research Program, CB# 3260, Smith Building, The University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-3260, or by e-mailing stat-or@unc.edu.
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 [181] DETERMINISTIC MODELS IN OPERATIONS RESEARCH (3). Prerequisite, MATH 547. Linear, integer, nonlinear and dynamic programming, classical optimization problems, network theory. Fall. Provan, Tolle.
445 [183] STOCHASTIC MODELS IN OPERATIONS RESEARCH (3). Prerequisite, BIOS 660 or STAT 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.
465 [185] SIMULATION ANALYSIS AND DESIGN (3). Prerequisite, STOR 435 (STAT 126). 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 [162] SHORT TERM ACTUARIAL MODELS (3). Prerequisite, STAT 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.
496 [090] INDEPENDENT STUDY. Prerequisite, permission of the instructor. This course is intended primarily for students working on honors projects.
497 [090] INDEPENDENT STUDY. Prerequisite, permission of the instructor.
515 [190] COMPUTATIONAL MATHEMATICS FOR DECISION SCIENCES (3). Prerequisite, 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.
582 [085] NEURAL NETWORK MODELS FOR THE DECISION AND COGNITIVE SCIENCES. Prerequisites, MATH 231 or STAT 155 or STOR 215 and permission of the instructor.
612 [210] MODELS IN OPERATIONS RESEARCH (3). Prerequisites, calculus, 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. 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.
641 [220] STOCHASTIC MODELS IN OPERATIONS RESEARCH I (3). Prerequisite, STAT 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, OR 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.
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 (Var.). Prerequisite, permission of the student's adviser. Fall and spring.
993 [393] MASTER'S THESIS (3 or more). Prerequisite, permission of the student's adviser. Fall. Staff.
994 [394] DOCTORAL DISSERTATION (3 or more). Prerequisite, permission of the student's adviser. Fall and spring. Staff.
The Statistics program offers a variety of courses of potential value to students majoring in other disciplines. The basic ideas of statistics are taught in STAT 355 and 356. Somewhat more theoretical and mathematical than STAT 355 and 356 are STAT 435 and 555.
Several of the program's other courses may be suitable for students from other departments. Interested students should contact the director of graduate studies or visit the department's Web page at www.stat-or.unc.edu.
The department offers both MS and PhD degrees in statistics. Students who plan to teach statistics or to engage in research of any kind should work for the degree of Doctor of Philosophy. This requires at least three years of full-time graduate work, predicated upon substantial undergraduate mathematical preparation. Research is an important part of the work for the doctorate. Those interested in obtaining an understanding of the fundamental notions of statistical theory and practice mainly through coursework are directed to the Master of Science degree program. This degree may be obtained with or without writing a thesis, and normally requires four semesters for completion. Doctoral students without an MS degree in statistics complete the MS program without delaying their PhD work.
The philosophy of the statistics program is that its PhD graduates should be broadly trained in statistical theory and practice and also be able to conduct basic research in some special area. Students in the first year typically take STAT 634-5, 654-5, and 664-5, and possibly other courses chosen from STAT 734-5 and 756-5. In the second and third years students taking advanced courses may specialize in an area of interest. Students may also take courses offered by other departments, such as the departments of Biostatistics and Mathematics, on the Chapel Hill campus, and by various departments at neighboring universities in the Research Triangle area, North Carolina State University in Raleigh and Duke University in Durham.
The Mathematics-Physics-Statistics Library, located in nearby Phillips Hall, maintains an extensive collection of books and journals pertaining to statistics.
The graduate curriculum in Statistics places strong emphasis on the mathematical theory of probability and statistics. 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 advanced (multivariable) calculus or real analysis, at least one semester in matrix algebra, and calculus-based courses in probability and statistics.
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. 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 and statistics.
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 $13,000 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, NC 27599-3260.
355 [101] STATISTICAL METHODS I (3). Prerequisite, STAT 155. Review of basic inference; 2-sample comparisons; correlation; introduction to matrices; simple and multiple regression (including significance tests, diagnostics, variable selection); analysis of variance; use of statistical software. Fall. Marron, Nobel, Zhu.
356 [102] STATISTICAL METHODS II (3). Prerequisite, STAT 355. Topics selected from: design of experiments; sample surveys; nonparametrics; time-series; multivariate analysis; contingency tables; logistic regression; simulation. Use of statistical software packages. Spring. Marron, Pipiras, Smith.
358 [104] SAMPLE SURVEY METHODOLOGY (BIOS 664) (3). 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.
496 [090] INDEPENDENT STUDY. Prerequisite, permission of the instructor. This course is intended primarily for students working on honors projects.
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.
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). Prerequisite, 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.
890, 891 [321, 322] SPECIAL PROBLEMS (3). Prerequisite, permission of the instructor.
930, 950 [331, 332] ADVANCED RESEARCH (3). Prerequisite, permission of the instructor.
940, 960 [310, 311] SEMINAR IN THEORETICAL STATISTICS (3). Prerequisite, STAT 655.
993 [392] MASTER'S PAPER (Var.). Prerequisite, permission of the student's adviser. Fall and spring. Staff.
994 [394] DOCTORAL DISSERTATION (Var.). Prerequisite, permission of the student's adviser. 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.