Statistics Department

STAT 401. Basic Statistics for Social and Life Sciences (3)
Introductory course primarily for graduate students in nursing and the health sciences. Statistical methods and applications using SPSS software. Display and summarization of data. Hypothesis testing and interval estimation. Not for credit toward undergraduate major or minor in statistics, nor for credit toward any graduate degree in statistics. Credit for only one of STAT 201, 401.

STAT 412. Statistics for Design and Analysis in Engineering and Science (3)
For graduate students (primarily) and advanced undergraduates in engineering, physical sciences, and life sciences. After basic statistical concepts are reviewed, the remainder of the course consists of a comprehensive introduction to statistical methods of designing experiments and analyzing data. The general objective is to train students in statistical modeling and in the choice of experimental designs to use in scientific investigations. A variety of experimental designs are covered, and regression analysis is presented as the primary technique for analyzing data from designed experiments, and in discriminating between various possible statistical models. The course is oriented toward graduate students engaged in or embarking on research. Prerequisite: MATH 122 (an introductory statistics course is recommended)

STAT 413. Reliability and Calibration (3)
Failure distributions related to life testing; extreme value distributions and their hazard functions. Static reliability of series, parallel and mixed systems. Coherent systems and system reliability approximations. Dynamic reliability models. Linear estimation, maximum likelihood, EM estimation, estimation from censored data. Calibration procedures. Distributions from uncalibrated processes, optimization of calibration procedures. Examples from industrial research and production processes. Prerequisite: one (1) of: STAT 244, 312, 313, 332, 333 or 433

STAT 414. Industrial Statistics (3)
Introduction to statistical methods and techniques that are being used in industry, and especially in various company-wide quality improvement programs such as Six Sigma. The course covers control charts and process capability with considerable breadth and depth. The classical and alternative approaches that have been used in designing industrial experiments are also covered extensively. Linear regression, analysis of means (ANOM), and evolutionary operation (EVOP) are other techniques that are covered. Prerequisite: STAT 312 or equivalent.

STAT 417. Theory of Interest and Life Contingencies (3)
For graduate students interested in actuarial science. Mathematical formulation for calculation of compound interest, present and accumulated values of single investments and of portfolios. Life table analysis for simple and multiple decrement functions. Life and special annuities; life insurance and reserves for life insurance. Statistical issues for prediction from actuarial models. Problem solving using actual insurance record data. Topics covered include areas examined in the American Society of Actuaries examination over ASA courses 150 and 160. Additional work is expected from graduate students. Prerequisite: MATH 223 and STAT 346 or STAT 446

STAT 425. Data Analysis and Linear Models (3)
Basic exploratory data analysis for univariate response with single or multiple covariates. Graphical methods and data summarization model-fitting using S-plus computing language. Linear and multiple regression. Emphasis on model selection criteria, on diagnostics to assess goodness of fit and interpretation. Techniques include transformation, smoothing, median polish, robust/resistant methods. Case studies, and analysis of individual data sets. Notes of caution and some methods for handling bad/biased data. Knowledge of regression is helpful. Prerequisite: Permission of Department.

STAT 426. Multivariate Analysis and Data Mining (3)
Extensions of exploratory data analysis and modeling to multivariate response observations and to non-Gaussian data. Singular value decomposition and projection, principal components, factor analysis and latent structure analysis, discriminant analysis and clustering techniques, cross-validation, E-M algorithm, and CART. Introduction to generalized linear modeling. Case studies of complex data sets with multiple objectives for analysis. Graduate students give both written and oral presentations of data analyses. Prerequisite: STAT 425

STAT 427. Statistical Computing (3)
Basic topics in statistical computing: Floating point arithmetic; Seminumerical computation including generation and tests of random numbers, Monte Carlo methods, variance reduction methods, stochastic models and simulation studies; numerical computation including numerical linear algebra, optimization and root-finding, numerical integration; some graphical and symbolic computations; special topics in statistical computing: resampling methods, EM algorithms, Gibbs sampling and projection pursuit. Prerequisite: STAT 345 or STAT 425 or permission of department.

STAT 433. Uncertainty in Engineering and Science (3)
Phenomena of uncertainty appear in engineering and science for various reasons and can be modeled in different ways. The course integrates the mainstream ideas in statistical data analysis with models of uncertain phenomena stemming from th ree distinct viewpoints: algorithmic/computational complexity; classical probability theory; and chaotic behavior of nonlinear systems. Descriptive statistics, estimation procedures and hypothesis testing (including design of experiments). Mathematica notebooks and simulations will be used. Note: Random number generators and their testing. Monte Carlo methods. Credit given for only on (1) of STAT 312, 313, 333, 133. Graduate students are required to do an extra project. Prerequisite: MATH 223 or MATH 122

STAT 437. Stochastic Modeling of Scientific Data (3)
Introduction to stochastic modeling of data. Emphasis on models and statistical analysis of data with a significant temporal and/or spatial structure. Markovian and semi-Markovian models, point processes, point cluster models, queuing model s, likelihood methods, estimating equations. Note: Restricted to declared graduate and undergraduate majors and minors in statistics and biostatistics only. Prerequisite: STAT 333 or STAT 433 (preferred) or STAT 325, STAT 425 , or STAT 445

STAT 445. Theoretical Statistics I (3)
Topics provide the background for statistical inference. Random variables; distribution and density functions; transformations, expectation. Common univariate distributions. Multiple random variables; joint, marginal and conditional distributions; hierarchical models, covariance. Distributions of sample quantities: distributions of sums of random variables, distributions of order statistics. Methods of statistical inference. Graduate students are responsible for mathematical derivations, and full proofs of principal theorems. Prerequisite: MATH 122 or MATH 223. Cross-listed as: EPBI 481.

STAT 446. Theoretical Statistics II (3)
Point estimation: maximum likelihood, moment estimators. Methods of evaluating estimators including mean squared error, consistency, "best" unbiased and sufficiency. Hypothesis testing; likelihood ratio and union-intersection tests. Properties of tests including power function, bias. Interval estimation by inversion of test statistics, use of pivotal quantities. Application to regression. Graduate students are responsible for mathematical derivations, and full proofs of principal theorems. Prerequisite: STAT 445 Cross-listed as: EPBI 482

STAT 448. Bayesian Theory with Applications (3)
Principles of Bayesian theory, methodology and applications. Methods for forming prior distributions using conjugate families, reference priors and empirically-based priors. Derivation of posterior and predictive distributions and their moments. Properties when common distributions such as binomial, normal or other exponential family distributions are used. Hierarchical models. Computational techniques including Markov chain Monte Carlo and importance sampling. Extensive use of applications to illustrate concepts and methodology. Prerequisite: STAT 445

STAT 453. Time Series, Wavelets I (3)
Stationary discrete-time and continuous-time models. Search for hidden periodicities in data. Fast Fourier transform; smoothing and filtering; spectra and periodograms. Multiple series; cross spectra and cross periodograms. Prediction problems. Time-frequency localization and the uncertainty principle, windowed Fourier transforms. Introduction to wavelet and multiresolution analysis. Prerequisite: one (1) of: STAT 333, 346, 433, 446

STAT 455. Linear Models (3)
Theory of least squares estimation, interval estimation and tests for models with normally distributed errors. Regression on dummy variables, analysis of variance and covariance. Variance components models. Model diagnostics. Robust regression. Analysis of longitudinal data. Prerequisite: MATH 201 and STAT 346 or STAT 446

STAT 466. Theory and Methods of Experimental Design (3)
(Also listed as EPBI 446). Experimental design for polynomial regression models and for multi-factor models. Theory for construction of increased efficiency designs including fractional factorials, Latin squares. Designs for response surfaces. GOSSETT-generated optimal designs for nonstandard problems. Knowledge of regression required. Prerequisite: STAT 425 Cross-listed as: EPBI 446

STAT 468. Sampling from Finite Populations: Theory and Applications (3)
(Also listed as EPBI 447). Introduction to the theory and methodology of sampling from finite populations. Simple random, stratified random, systematic and multistage cluster sampling. Linear, ratio and regression estimators. Methodology for handling missing data, inference for small geographical areas or for small subpopulations, inference for quantiles. Application to large-scale personal interview and telephone surveys. Prerequisite: STAT 345 or STAT 445 Cross-listed as: EPBI 447

STAT 471. Special Topics in Statistics (1- 3)
Topics in specialized areas of statistical theory and methodology, with emphasis on recent advances in theory and development of new methodology. Topics may change from year to year. Number of credit hours for the class will be predetermined each semester based on the material to be presented. Consent of the instructor required.

STAT 476. Advances in Statistics and Modeling (1- 3)
Topics in specialized areas of statistics and stochastic modeling, with emphasis on recent advances in theory and formulation of models. Investigation of new areas of application for statistical or stochastic models. Topics may change from year to year. Number of credit hours for the class will be predetermined each semester based on the material to be presented. Consent of the instructor required.

STAT 491. Graduate Student Seminar (1- 2)
Seminar run collaboratively by graduate students to investigate an area of current research, the topic chosen each semester. All graduate students participate in presentation of material each semester. Satisfies requirement for every full-time graduate student to enroll in a participatory seminar every semester while registered in any graduate degree program. Graduate standing required.

STAT 495A. Consulting Forum (1-3)
This course examines the principles of statistical consulting. Included are the views and practices of prominent statistical consultants, as obtained from the literature and from other sources. This includes responsibilities of the consultant and of the client. Role playing is used in an attempt to simulate actual consulting scenarios. The course also serves to unify what the students have learned in their course work in preparation for applying their knowledge in consulting work. Prerequisite: STAT 325 or STAT 425

STAT 495B. Consulting Forum with Practicum (3)
Graduate students become involved in actual consulting projects under the guidance of the instructor. The students' involvement can result from consulting problems presented by guest lecturers, or by assisting the instructor on projects that have come to the department. The students gain experience in report writing. The importance of communicating the results of a study at the appropriate statistical level for the client is stressed. Prerequisite: STAT 325 or STAT 425

STAT 525. Advanced Data Analysis (3)
Topics drawn from resampling methods (including bootstrapping), MCMC (Gibbs sampling), nonparametric curve and surface fitting, kernel density estimation, projection pursuit, mixture models, time series (time permitting), approaches to model uncertainty, models for repeated measures and structural-functional models, statistical inference for large systems, modern data analysis techniques. Prerequisite: STAT 426 or permission of department.

STAT 527. Advanced Statistical Computing (3)
Special topics drawn from statistical computing, complex system and dynamic computation. Oriented to research. Prerequisite: STAT 427

STAT 537. Advanced Stochastic Modeling of Scientific Data I (3)
Spatial statistics. Theory and techniques for spatial or spatial-temporal relationships in high dimensional data, point pattern analysis, estimation of spatial covariance either stationary or non-stationary in space, applications to environ mental sciences. Characterizations and solutions for mapping problems, for image reconstruction, for analysis of fractal spatial-temporal processes with particular application to environmental sciences. Prerequisite: STAT 446 and STAT 437

STAT 538. Advanced Stochastic Modeling of Scientific Data II (3)
Foundations of discrete and continuous-time dynamical systems. Complexity of nonlinear dynamical systems. Descriptive statistics of dynamical systems, invariant densities and their estimation. Ergodic properties, space and time-averaging. Chaotic behavior. Fractals as a signature of chaos. Statistical estimation of fractal dimension. Asymptotic fluctuations in dynamical systems. Statistical problems in physical sciences; statistical hydrodynamics. Statistical problems for hydrological, atmospheric and oceanic models. Theoretical foundations of simulation of random phenomena. Prerequisite: STAT 437

STAT 545. Advanced Theory of Statistics I (3)
A systematic development of advanced statistical theory. Background concepts. Limits, order comparisons, convergence. Sample moments, quantiles and other statistics. Transformations. Characterization of distribution functions and characteristic functions. Normal and other approximations to distributions. Quadratic forms and other functions of asymptotically normal statistics. Asymptotic properties of statistics including asymptotic efficiency, consistency. Admissibility, sufficiency and ancillarity. Nuisance parameters, parameter orthogonality. Distribution theory in nuisance parameters. Prerequisite: STAT 446

STAT 546. Advanced Theory of Statistics II (3)
Estimation: maximum likelihood, minimax, Bayes', empirical Bayes', and James-Stein estimators. Entropy and information. U-statistics and their distributions. Von Mises differentiable statistical functions, M, L, R-estimators. Confidence intervals and regions. Simple and weighted empirical processes. Convergence and distributions for empirical processes. Prerequisite: STAT 545

STAT 547. Advanced Theory of Statistics III (3)
Development of empirical process theory with application to censored data with random, fixed or arbitrary censoring mechanism. Characterization of quantile processes, spacings and large deviations as empirical processes. Asymptotic results for nonparametric regression, bootstrap and other resampling estimators. Prerequisite: STAT 546.

STAT 553. Time Series and Wavelets II (3)
Advanced topics in time series including nonstationary series, nonlinear models. In-depth development and application of wavelet theory. Wavelets as computational tool. Extensive use of computing to illustrate and investigate modeling with wavelets. Prerequisite: STAT 453 and STAT 446 and MATH 491.

STAT 555. Generalized Linear Models (3)
Generalization from linear statistical models to discrete responses and other non-Gaussian cases. Theory for binomial proportions and logits, Poisson counts and loglinear models, multinomial response models, models of survival data. Analysis of deviance, model checking. Conditional, marginal and quasi-likelihood methods. Inverse linear models. Generalized linear mixed models. Prerequisite: STAT 455.

STAT 571. Advanced Topics in Statistics (1- 3)
For advanced graduate students. Topics in specialized areas of statistical theory and methodology, with emphasis on recent advances in theory, developments of new methodology and definition of new research questions. Topics may change from year to year. Number of credit hours for the class will be predetermined each semester based on the material to be presented. Consent of the instructor required.

STAT 576. Advanced Topics in Modeling (1- 3)
Advanced topics in specialized areas of statistics and stochastic modeling designed to define new research directions drawing on recent advances in theory and model formulation. Focus on statistical issues arising in the application of statistical or stochastic models to new substantive research efforts. Topics may change from year to year. Number of credit hours for the class will be predetermined each semester based on the material to be presented. Consent of the instructor required.

STAT 591. Statistical Research Seminar (1- 3)
Seminar to prepare and explore current research topics presented by faculty and invited statistics colloquium speakers. Graduate students lecture on background material for colloquia using recent publications. Following each colloquium, stu dents lead discussion and clarify further the contributions of the research. Newer students are paired with senior students; colloquium assignments coincide with students' research interests insofar as possible. Attendance at statistics colloquia is required. Satisfies requirement for every full-time graduate student to enroll in a participatory seminar every semester while registered in any graduate degree program. Number of credit hours will be determined by prior agreement with the instructor and depends on the extent of the student's responsibility. Consent of the instructor required.

STAT 601. Reading and Research (1- 9)
Individual study and/or project work. Permission of instructor required.

STAT 621. M. S. Research Project (1- 9)
Substantial and/or nonstandard statistical techniques which leads to results suitable for publication. Written project report must present the context for the research, justify the statistical methodology used, draw appropriate inferences and interpret these inferences in both statistical and substantive scientific terms. Oral presentation of research project may be given in either graduate student seminar of consulting forum. Permission of instructor required.

STAT 651. Thesis M.S. (1-36)
(Credit as arranged) May be used as alternative to STAT 621 in fulfillment of requirements for M.S. degree in statistics. Permission of instructor required.

STAT 701. Appointed Dissertation Fellowship (1-36)