Course Descriptions
Department of Statistics
J. A. Calvin, R. J. Carroll, W. Chen, D. B. H. Cline, A. Dabney, D. Dahl, P. F. Dahm*, R. Fan, R. J. Freund, C. E. Gates, M. Genton, J. D. Hart, R. R. Hocking, J. Huang, O. C. Jenkins, M. Jun, S. Lahiri, E. Li, F. Liang, J. Lim, M. T. Longnecker, Y. Ma, B. K. Mallick, J. H. Matis, J. F. McNamara, Y. Mu, U. Muller, H. J. Newton, E. Parzen, S. S. Rao, L. J. Ringer, S. Sheather (Head), M. Sherman, S. Sinha, W. B. Smith, F. M. Speed, C. H. Spiegelman, M. Vannucci, N. Wang, S. Wang, T. E. Wehrly, W. West, L. Zhu, J. Zinn
* Graduate Advisor
The Department of Statistics offers a graduate program leading to the degrees of Master of Science or Doctor of Philosophy. The department cooperates closely with all subject matter area departments in setting up flexible minor programs in statistics.
The Department of Statistics offers two options in its master’s degree programs: (1) the MS (thesis option) which requires the preparation of a thesis and, (2) the MS (non-thesis option) which requires more formal course work in lieu of the thesis. Both programs provide a balanced training in statistical methods and statistical theory and are intended to prepare the student to adapt statistical methodologies to practical problems.
The aim of the PhD program is to provide comprehensive and balanced training in statistical methods and statistical theory. Particular emphasis will be placed on training students to independently recognize the relevance of statistical methods to the solution of specific problems and to enable them to develop new methods when they are needed. The training will also aim at conveying a sound knowledge of existing statistical theory, including the mathematical facility to develop new results in statistical methodology. At the same time, the program will be kept sufficiently flexible to permit students to develop their specific interests.
The following courses are offered on an irregular basis: STAT 605, 606, 609, 627, 634, 635, 637, 671, and 673. Contact the department for specific offerings for any given term.
Statistics
(STAT)
601. Statistical Analysis. (3-2). Credit 4.
For students in engineering, physical and mathematical sciences. Introduction to probability, probability distributions and statistical inference; hypotheses testing; introduction to methods of analysis such as tests of independence, regression, analysis of variance with some consideration of planned experimentation. Prerequisite: MATH 152 or 172.
602. Statistical Methods of Regression Analysis. (3-0). Credit 3.
Linear, nonlinear, nonparametric and logistic regressions; methodologies and their statistical foundations for detection of collinearity, outliers and correlation in errors or independent variables. Prerequisites: STAT 601 or 641; STAT 610; MATH 423 or equivalent.
604. Special Problems in Statistical Computations and Analysis. (3-0). Credit 3.
Computer algorithms for programming; statistical analysis, efficient uses of existing statistical computer programs, generation of random numbers and statistical variables, programming of simulation studies, selected topics in statistical analysis not covered in STAT 601. Prerequisite: STAT 601 or concurrent enrollment in STAT 610 and 641.
605. Advanced Topics in Computational Statistics. (3-0). Credit 3.
Algorithms in constrained and unconstrained optimization; time series analysis; multivariate analysis; use and development of modern graphical exploratory data analysis; methods for interfacing programs with existing computer environments. Prerequisite: STAT 604.
606. Design of Experiments. (3-0). Credit 3.
Fundamental concepts in the design of experiments, justification of linear models, randomization, principles of blocking and the use of concomitant observations; construction and analysis of basic designs including confounding, fractional replication, composite designs and incomplete block designs. Prerequisite: STAT 642 or 653 or approval of instructor.
607. Sampling. (3-0). Credit 3.
Planning, execution and analysis of sampling from finite populations; simple, stratified, multistage and systematic sampling; ratio estimates. Prerequisite: STAT 601 or 652 or concurrent enrollment in STAT 641.
608. Regression Analysis. (3-0). Credit 3.
Multiple, curvilinear, nonlinear, robust, logistic and principal components regression analysis; regression diagnostics, transformations, analysis of covariance. Prerequisite: STAT 601 or 641.
609. Order Statistics and Non-Parametric Methods. (3-0). Credit 3.
Multiple, curvilinear, nonlinear, robust, logisit. Prerequisite: STAT 601, 641 or 652.
610. Theory of Statistics – Distribution Theory. (3-0). Credit 3.
Brief introduction to probability theory; distributions and expectations of random variables, transformations of random variables and order statistics; generating functions and basic limit concepts. Prerequisite: MATH 409 or concurrent enrollment in MATH 409.
611. Theory of Statistics – Inference. (3-0). Credit 3.
Theory of estimation and hypothesis testing; point estimation, interval estimation, sufficient statistics, decision theory, most powerful tests, likelihood ratio tests, chi-square tests. Prerequisite: STAT 610 or equivalent.
612. Theory of Linear Models. (3-0). Credit 3.
Theory of least squares, theory of general linear hypotheses and associated small sample distribution theory, analysis of multiple classifications. Prerequisites: STAT 611 or equivalent; MATH 423.
613. Advanced Theory of Statistical Inference. (3-0). Credit 3.
General theory of estimation and sufficiency including maximum likelihood and minimum variance estimation; Neyman-Pearson theory of testing hypotheses; elements of decision theory. Prerequisites: STAT 611; MATH 409.
614. Statistical Applications in Probability. (3-0). Credit 3.
Probability measures; Lebesque-Stieltjes integration, sigma fields, random variables, expectation, moment inequalities, independence, convergence of random variables and sample moments, characteristics functions, convergence of distributions, the central limit theorem and the delta method. Prerequisite: STAT 610.
615. Stochastic Processes. (3-0). Credit 3.
Survey of the theory of Poisson processes, discrete and continuous time Markov chains, renewal processes, birth and death processes, diffusion processes and covariance stationary processes. Prerequisites: STAT 611; MATH 409.
616. Multivariate Analysis. (3-0). Credit 3.
Multivariate normal distributions and multivariate generalizations of classical test criteria, Hotelling’s T2, discriminant analysis and elements of factor and canonical analysis. Prerequisites: STAT 611 and 612.
620. Statistical Large Sample Theory. (3-0). Credit 3.
Transformations of statistics; statistical functionals including influence curves and M, L and R estimators; u-statistics; asymptotic properties of estimators; asymptotic properties of tests; order of stochastic convergence; Edgeworth expansions and the bootstrap. Prerequisites: STAT 613 and 614 or approval of instructor.
623. Statistical Methods for Chemistry. (3-0). Credit 3.
Chemometrics topics of process optimization, precision and accuracy; curve fitting; chi-squared tests; multivariate calibration; errors in calibration standards; statistics of instrumentation. Prerequisite: STAT 601, 641 or 652 or approval of instructor.
626. Methods in Time Series Analysis. (3-0). Credit 3.
Introduction to statistical time series analysis; autocorrelation and spectral characteristics of univariate, autoregressive, moving average models; identification, estimation and forecasting. Prerequisite: STAT 601 or 642 or approval of instructor.
627. Nonparametric Function Estimation. (3-0). Credit 3.
Nonparametric function estimation; kernel, local polynomials, Fourier series and spline methods; automated smoothing methods including cross-validation; large sample distributional properties of estimators; recent advances in function estimation. Prerequisite: STAT 611.
630. Overview of Mathematical Statistics. (3-0). Credit 3.
Basic probability theory including distributions of random variables and expectations. Introduction to the theory of statistical inference from the likelihood point of view including maximum likelihood estimation, confidence intervals, and likelihood ratio tests. Introduction to Bayesian methods. Prerequisites: MATH 221, 251, and 253.
632. Statistical Decision Theory. (3-0). Credit 3.
Fundamentals of Bayesian inference, single and multi-parameter models, Bayesian regression and linear models, posterier simulation, MCMC, hierarchical models. Prerequisite: STAT 611 or approval of instructor.
634. Response Surface Design and Analysis. (3-0). Credit 3.
Definition of response surface and relation to multiple regression; ridge analysis; first, second and third order designs for response surface estimation; optimization of response surface designs for various criteria; the Box-Draper theory and EVOP. Prerequisite: STAT 608.
635. Application of Stochastic Processes to the Natural Sciences. (3-0). Credit 3.
Basic concepts, Random walks, Markov chains, branching processes, Markov processes in continuous time, homogeneous and nonhomogeneous processes, multi-dimensional processes, queuing processes, epidemic processes, competition and predation, diffusion and non-Markovian processes. Prerequisite: STAT 610 or approval of instructor.
636. Methods in Multivariate Analysis. (3-0). Credit 3.
Multivariate extensions of the chi-square and t-tests, discrimination and classification procedures; applications to diagnostic problems in biological, medical, anthropological and social research; multivariate analysis of variance, principal component and factor analysis, canonical correlations. Prerequisites: MATH 423 and STAT 653 or approval of instructor. Cross-listed with INFO 657.
637. Statistical Methods in Ecology. (3-0). Credit 3.
Derivation and application of statistical distributions for sampling models, birth-death processes, time intervals, size models, heterogeneous and clustered models in ecology; stochastic models for population growth, competition and predation and multi-dimensional processes. Prerequisite: STAT 601, 641 or 652 with approval of instructor.
641. The Methods of Statistics I. (3-0). Credit 3.
An application of the various disciplines in statistics to data analysis, introduction to statistical software; demonstration of interplay between probability models and statistical inference. Prerequisite: Concurrent enrollment in STAT 610 or approval of instructor.
642. The Methods of Statistics II. (3-0). Credit 3.
Design and analysis of experiments; scientific method; graphical displays; analysis of nonconventional designs and experiments involving categorical data. Prerequisites: STAT 610 and 641.
643. Biostatistics I. (3-0). Credit 3.
Bio-assay for quantitative and quantal responses: statistical analysis of contingency, including effect estimates, matched samples and misclassification. Prerequisites: STAT 608 and 642.
644. Biostatistics II. (3-0). Credit 3.
Generalized linear models; survival analysis with emphasis on nonparametric models and methods. Prerequisite: STAT 643 or approval of instructor.
647. Spatial Statistics. (3-0). Credit 3.
Spatial correlation and its effects; spatial prediction (kriging); spatial regression; analysis of point patterns (tests for randomness and modelling patterns); subsampling methods for spatial data. Prerequisite: STAT 601 or 611 or equivalent.
651. Statistics in Research I. (3-0). Credit 3.
For graduate students in other disciplines; non-calculus exposition of the concepts, methods and usage of statistical data analysis; T-tests, analysis of variance and linear regression. Prerequisite: MATH 102 or equivalent.
652. Statistics in Research II. (3-0). Credit 3.
Continuation of STAT 651. Concepts of experimental design, individual treatment comparisons, randomized blocks and factorial experiments, multiple regression, Chi-squared tests and a brief introduction to covariance, non-parametric methods and sample surveys. Prerequisite: STAT 651.
653. Statistics in Research III. (3-0). Credit 3.
Advanced topics in ANOVA; analysis of covariance; and Regression Analysis including analysis of messy data; non-linear regression; logistic and weighted regression; diagnostics and model building; emphasis on concepts; computing and interpretation. Prerequisite; STAT 652
655. Forecasting Methods and Applications. (3-0). Credit 3.
Development of statistical models for describing business trends and economic fluctuations, generation of forecasts and error limits, evaluation of forecasts; applications to economic data arising in business. Classification 6 students may not enroll in this course. Prerequisite: STAT 652 or equivalent or approval of instructor. Cross-listed with INFO 655.
657. Advanced Programming Using SAS. (3-0). Credit 3.
Programming with SAS/IML, programming in SAS Data step, advanced use of use of various SAS procedures. Prerequisite: STAT 642.
658. Transportation Statistics. (3-0). Credit 3.
Design of experiments, estimation, hypothesis testing, modeling, and data mining for transportation specialists. Prerequisite: STAT 211 or STAT 651.
659. Applied Categorical Data Analysis. (3-0). Credit 3.
Introduction to analysis and interpretation of categorical data using ANOVA/regression analogs; includes contingency tables, loglinear models, logistic regression; use of computer software such as SAS, GLIM, SPSSX. Prerequisite: STAT 601, 641 or 652 or equivalent.
661. Statistical Genetics I. (3-0). Credit 3.
Basic concepts in human genetics, sampling designs, gene frequency estimation, Hardy-Weinberg equilibrium, linkage disequilibrium, association and transmission disequilibrium test studies, linkage and pedigree analysis, segregation analysis, polygenic models, DNA sequence analysis. Prerequisites: STAT 610 and 611.
665. Statistical Applications of Wavelets. (3-0). Credit 3.
This is a course on the use of wavelet methods in statistics. The course introduces wavelet theory, provides an overview of wavelet-based statistical methods. Topics include smoothing of noisy signals, estimation of function data and representation of stochastic processes. Some emphasis is given to Bayesian procedures. Prerequisite: STAT 611 or approval by the instructor.
667. Statistics for Advanced Placement Teachers. (3-0). Credit 3.
Review of the fundamental concepts and techniques of statistics; topics included in Advanced Placement Statistics; exploring data, planning surveys and experiments, exploring models, statistical inference. Prerequisite: Approval of instructor.
671. Methods of Statistical Data Modeling I. (3-0). Credit 3.
Introduction to new methods of statistical analysis, especially statistical data modeling, exploratory data analysis, adaptive and robust estimation. Prerequisite: STAT 611 or equivalent.
673. Time Series Analysis I. (3-0). Credit 3.
Introduction to diverse modes of analysis now available to solve for univariate time series; basic problems of parameter estimation, spectral analysis, forecasting and model identification. Prerequisite: STAT 611 or equivalent.
681. Seminar. (1-0). Credit 1.
Oral presentations of special topics and current research in statistics. May be repeated for credit. Prerequisite: Graduate classification in statistics.
684. Professional Internship. Credit 1 to 3.
Practicum in statistical consulting for students in PhD program. Students will be assigned consulting problems brought to the Department of Statistics by researchers in other disciplines. Prerequisite: Master’s in statistics or equivalent.
685. Directed Studies. Credit 1 to 6.
Individual instruction in selected fields in statistics; investigation of special topics not within scope of thesis research and not covered by other formal courses. Prerequisites: Graduate classification and approval of department head.
689. Special Topics in... Credit 1 to 4.
Selected topics in an identified area of statistics. Open to non-majors. May be repeated for credit. Prerequisite: Approval of instructor.
691. Research. Credit 1 or more.
Research for thesis or dissertation. Prerequisite: Graduate classification.
See Econometrics for descriptions of related courses.