# Statistics (STAT)

### Applied and Engineering Statistics

250/IT 250 Introductory Statistics I (3:3:0). Prerequisite: High school algebra. Elementary introduction to statistics. Topics include descriptive statistics, probability, estimation and hypothesis testing for means and proportions, correlation, and regression. Students use statistical software for assignments. f,s,sum

344 Probability and Statistics for Engineers and Scientists I (3:3:0). Prerequisite: MATH 213. Introduction to probability and statistics with applications to computer science, engineering, operations research, and information technology. Basic concepts of probability, random variables and expectation, Poisson process, bivariate distributions, sums of independent random variables, correlation and least squares estimation, central limit theorem, sampling distributions, maximum likelihood and unbiased estimators, confidence interval construction, and hypothesis testing.f,s,sum

346 Probability for Engineers (3:3:0). Prerequisite: Math 213. Introduction to probability with applications to electrical and computer engineering, operations research, information technology, and economics. Basic concepts of probability, conditional probability, random variables and moments, specific probability distributions, multivariate distributions, moment generating functions, limit theorems, and sampling distributions. f,s

350 Introductory Statistics II (3:3:0). Prerequisite: STAT 250. Emphasis on applications. Topics include analysis of variance, multiple regression, and nonparametric inference. A statistical computer package is used for data analysis. s

354 Probability and Statistics for Engineers and Scientists II (3:3:0). Prerequisite: STAT 344. Continuation of STAT 344. Multivariate probability distributions, variable transformations, regression, analysis of variance, contingency tables, and nonparametric methods. Applications to quality control, acceptance sampling, and reliability. s

362/IT 362 Introduction to Computer Statistical Packages (3:3:0). Prerequisite: STAT 250/IT 250 or equivalent. Use of computer packages in the statistical analysis of data. Topics include data entry, checking, and manipulation, as well as the use of computer statistical packages for regression and analysis of variance. f

455 Experimental Design (3:3:0). Prerequisite: STAT 350 or 354, and STAT 362 or 501. Principles of analysis of variance and experimental design. Topics include computation and interpretation of analysis of variance; multiple comparisons; orthogonal contrasts; design of experiments including factorial, hierarchical, and split plot designs; principles of blocking and confounding in 2**n experiments; estimation of variance components. Optional topics may include analysis of covariance, partial hierarchical designs, or incomplete block designs. Computer statistical packages are used to perform computations. a,s

457 Applied Nonparametric Statistics (3:3:0). Prerequisites: STAT 350 or 354, or equivalent. Introduction to nonparametric methods with applications to the decision and information sciences and operations analysis. Topics covered are testing and estimation for one- and two-sample problems, independent and paired samples, location and dispersion problems, one- and two-way layouts, tests for independence, regression, and discussion of efficiency. af

463 Introduction to Exploratory Data Analysis (3:3:0). Prerequisite: STAT 350 or 354, or equivalent. Introduction to modern exploratory data analysis techniques. Topics include graphical techniques, such as box plots, parallel coordinate plots, and other graphical devices, re-expression and transformation of data, order statistics, influence and leverage, and dimensionality reduction methods such as projection pursuit. f

474 Introduction to Survey Sampling (3:3:0). Prerequisite: STAT 350 or 354, and STAT 362 or 501. Introduction to the design and analysis of sample surveys. Sample designs covered include simple random sampling; systematic sampling; stratified, cluster, and multistage sampling. Analytical methods include sample size determination, ratio and regression estimation, imputation for missing data, and nonsampling error adjustment. Practical problems encountered in conducting a survey are discussed. Methods are applied to case studies of actual surveys. Class project may be required. Course is recommended for students of decision, information, social sciences, and mathematics. f

498 Independent Study in Statistics (1-3:0:0). Prerequisite: 60 undergraduate credits; must be arranged with instructor and approved by the department chair before registering. Directed self-study of special topics of current interest in statistics. May be repeated for a maximum of six credits if topics are substantially different.

499 Special Topics in Statistics (3:3:0). Prerequisites: 60 undergraduate credits and permission of instructor; specific prerequisites vary with the nature of the topic. Topics of special interest to undergraduates. May be repeated for a maximum of six credits if the topics are substantially different.

501 SAS Language and Basic Procedures (1:1:0). Prerequisites: A course in statistics and experience with Microsoft Windows. Introduction to the SAS Data Step and Base SAS Procedures. Preparation for graduate students in the use of SAS for other graduate courses offered by the Applied and Engineering Statistics Department. Topics include observation and variable structures, data interfaces, formats, functions, and procedures for summarizing and displaying data. At most, one of STAT 501­503 can be applied toward the MS or certificate programs in statistics. f

502 Introduction to SAS/GRAPH (1:1:0). Prerequisite STAT 501. Introduction to SAS/GRAPH. Continued preparation beyond STAT 501 for graduate students in the use of SAS for other graduate courses offered by the Applied and Engineering Statistics Department. Topics include an overview of SAS/GRAPH and SAS/GRAPH procedures, SAS/GRAPH output options and in-depth coverage of the GOPTIONS, GDEVICE, GCHART, GPLOT and GSLIDE procedures. At most, one of STAT 501­503 can be applied toward the MS or certificate programs in statistics. f

503 SAS Macro Language (1:1:0). Prerequisite: STAT 501. Introduction to SAS Macro Language. Continued preparation beyond STAT 501 for graduate students in the use of SAS for other graduate courses offered by the Applied and Engineering Statistics Department. Topics include an overview of macro language processing, macro variables, defining and calling macro variables, macro quoting, macro facility error messages, and examples of efficient code using macros. At most, one of STAT 501­503 can be applied toward the MS or certificate programs in statistics. f

510 Statistical Foundations for Technical Decision Making (3:3:0). Prerequisite: MATH 108 or equivalent, or permission of instructor. Use of statistical methods as scientific tools in the analysis of practical problems. Topics include descriptive statistics, probability, distributions, sampling, inference, estimation and hypothesis testing; linear regression and correlation; the analysis of variance; multiple regression; and the analysis of association between categorical variables. Credits are not applicable toward the MS in Statistical Science, but can be used to satisfy the requirements for the certificate in Federal Statistics. Certificate program students will be granted credit for only one of STAT 510, 535, or 554. s

530 Mathematical Methods for Statistics and Engineering (3:3:0). Prerequisite: MATH 113 or 108. Calculus and probability results required for the pursuit of an advanced degree in statistics or a related field. Cannot be used to satisfy the requirements of the MS in Statistical Science. Designed for students who have not completed the MATH 113-114-213 sequence or need a refresher course.f

535 Analysis of Experimental Data (3:3:0). Prerequisite: STAT/IT 250 or equivalent. Statistical methods for the analysis of experimental data, including ANOVA and regression. Parametric and nonparametric inference methods appropriate for a variety of experimental designs are presented along with the use of appropriate statistical software. Intended primarily for researchers in the natural sciences. Course can be used to satisfy the requirements for the Certificate in Federal Statistics, but not the MS in Statistical Science. Certificate program students will be granted credit for only one of STAT 510, 535, or 554. f

544 Applied Probability (3:3:0). Prerequisite: STAT 344 or equivalent, or permission of instructor. Course in probability with applications in computer science, engineering, operations research, and statistics. Random variables and expectation, conditional expectation, random vectors, special distributions, limit theorems, and simulation are covered. f,s

554 Applied Statistics (3:3:0). Prerequisite: STAT 344 or equivalent, or permission of instructor. Application of basic statistical techniques. Focus is on the problem (data analysis) rather than on the theory. Topics include one and two sample tests and confidence intervals for means and medians, descriptive statistics, goodness-of-fit tests, one- and two-way ANOVA, simultaneous inference, testing variances, regression analysis, and categorical data analysis. Normal theory is introduced first with discussion of what happens when assumptions break down. Alternative robust and nonparametric techniques are presented. Course can be used to satisfy the requirements for the Certificate in Federal Statistics, but not the MS in Statistical Science. Certificate program students will be granted credit for only one of STAT 510, 535, or 554. f,s

574 Survey Sampling I (3:3:0). Prerequisite: STAT 354 or 554; corequisite: STAT 362 or 501. Design and implementation of sample surveys. Covers components of a survey; probability sampling designs to include simple random, systematic, Bernoulli, proportional to size, stratified, cluster and two-stage sampling; and ratio and regression estimators. Practical problems encountered in conducting a survey are discussed. Methods are applied to case studies of actual surveys. Class project is required. f

634 Case Studies in Data Analysis (3:3:0). Prerequisite: STAT 554 and 501 or permission of instructor. Examination of a wide variety of case studies illustrating data-driven model building and statistical analysis. With each case study, various methods of data management, data presentation, statistical analysis, and report writing are compared. su

645 Stochastic Processes (3:3:0). Prerequisite: OR 542, STAT 544, or permission of instructor. Selected applied probability models including Poisson processes, discrete- and continuous-time Markov chains, renewal and regenerative processes, semi-Markov processes, queuing and inventory systems, reliability theory, and stochastic networks. Emphasis is on applications in practice as well as analytical models.

652 Statistical Inference (3:3:0). Prerequisite: STAT 544 or ECE 528 or equivalent. Fundamental principles of estimation and hypothesis testing. Topics include limiting distributions and stochastic convergence, sufficient statistics, exponential families, statistical decision theory and optimality for point estimation, Bayesian methods, maximum likelihood, asymptotic results, interval estimation, optimal tests of statistical hypotheses, and likelihood ratio tests. s

655 Analysis of Variance (3:3:0). Prerequisite: STAT 554 and 501or permission of instructor. Single and multifactor analysis of variance, planning sample sizes, introduction to the design of experiments, random block and Latin square designs, and analysis of covariance. as

656 Regression Analysis (3:3:0). Prerequisites: STAT 554, 501 or permission of instructor and matrix algebra. Simple and multiple linear regression, polynomial regression, general linear models, subset selection, step-wise regression, and model selection. Also covered are multicollinearity, diagnostics, and model building. Both the theory and practice of regression analysis are covered. f

657 Nonparametric Statistics (3:3:0). Prerequisite: STAT 554. Distribution-free procedures for making inferences about one or more samples. Tests for lack of independence, for association or trend, and for monotone alternatives are included. Measures of association in bivariate samples and multiple classifications are discussed. Both theory and applications are covered. Students are introduced to appropriate statistical software. af

658 Time Series Analysis and Forecasting (3:3:0). Prerequisite: STAT 652 or 554 or equivalent. Modeling stationary and nonstationary processes, autoregressive, moving average and mixed model processes, hidden periodicity models, properties of models, autocovariance functions, autocorrelation functions, partial autocorrelation functions, spectral density functions, identification of models, estimation of model parameters, and forecasting techniques.af

662 Multivariate Statistical Methods (3:3:0). Prerequisite: STAT 554 or equivalent and STAT 501 or permission of instructor. Standard techniques of applied multivariate analysis. Topics include review of matrices, Tsquare tests, principle components, multiple regression and general linear models, analysis of variance and covariance, multivariate ANOVA, canonical correlation, discriminant analysis, classification, factor analysis, clustering, and multidimensional scaling. Computer implementation via a statistical package is an integral part of the course. as

663/CSI 773 Statistical Graphics and Data Exploration (3:3:0). Prerequisite: A 300-level course in statistics; STAT 554 strongly recommended. Exploratory data analysis provides a reliable alternative to classical statistical techniques that are designed to be the best possible when stringent assumptions apply. Topics covered include graphical techniques such as scatter plots, box plots, parallel coordinate plots and other graphical devices, re-expression and transformation of data, influence and leverage, and dimensionality reduction methods such as projection pursuit. f

664/SYST 664 Bayesian Inference and Decision Theory (3:3:0). Prerequisite: STAT 544 or 554 or equivalent, or permission of instructor. This course introduces students to decision theory and its relationship to Bayesian statistical inference. Students will learn the commonalities and differences between the Bayesian and frequentist approaches to statistical inference, how to approach a statistics problem from the Bayesian perspective, and how to combine data with informed expert judgment in a sound way to derive useful and policy relevant conclusions. Students will learn the necessary theory to develop a firm understanding of when and how to apply Bayesian and frequentist methods, and will also learn practical procedures for inference, hypothesis testing, and developing statistical models for phenomena. Specifically, students will learn the fundamentals of the Bayesian theory of inference, including probability as a representation for degrees of belief, the likelihood principle, the use of Bayes Rule to revise beliefs based on evidence, conjugate prior distributions for common statistical models, and methods for approximating the posterior distribution. Graphical models are introduced for constructing complex probability and decision models from modular components. as

665 Categorical Data Analysis (3:3:0). Prerequisite: STAT 554 or equivalent and STAT 501. Analysis of cross-classified categorical data in two and higher dimensions. Familiarity with the basic test for two-way contingency tables and elementary regression and analysis of variance as presented in STAT 554 is presumed. Topics include measures of association, logistic regression, linear response models, loglinear models, repeated measurements data, and analy sis of incomplete tables. A computer statistical package is used extensively for data analysis. as

668 Survival Analysis (3:3:0). Prerequisites: STAT 544, STAT 554 or STAT 535, and STAT 501 or a working knowledge of SAS. Survival Analysis is a class of statistical methods for studying the occurrence and timing of events. In medical research, the events may be deaths and the objective is to determine the factors affecting survival times of patients following treatment, usually in the setting of clinical trials. The methods can also be applied to the social and natural sciences and engineering where they are known by other names (reliability, event history analysis, etc.). The concepts of censored data, time-dependent variables, and survivor and hazard functions are central. Nonparametric methods for comparing two or more groups of survival data are studied. The Cox regression model (proportional hazards model), Weibull model, and the accelerated failure time model are studied in detail. Concepts are applied to the analysis of real data from major medical studies using SAS software. af

673 Statistical Methods for Longitudinal Data Analysis (3:3:0). Prerequisite: STAT 674 or permission of instructor. Principles of the design and analysis of longitudinal studies. Topics include retrospective and prospective studies, repeated periodic and continuous surveys, rotating of panel surveys, management of a longitudinal database, estimation of the level and change of population means, and proportions and totals over time. Techniques include the classical minimum variance unbiased estimators, time series analysis, and model-based multivariate analysis. Case studies such as the Current Population Survey and the National Crime Survey are presented. ir

674 Survey Sampling II (3:3:0). Prerequisites: STAT 501, 554 and 574. Continuation of STAT 574. Regression estimators for complex sampling designs, domain estimation, two-phase sampling, weighting adjustments for nonresponse, imputation, nonresponse models, measurement error models, introduction to variance estimation. Applications to case studies of actual surveys are made. as

677/OR 677/SYST 677 Statistical Process Control (3:3:0). Prerequisite: STAT 554, 610, or equivalent. See OR 677.

678/OR 675 Reliability Analysis (3:3:0). Prerequisite: STAT 554 or equivalent. Introduction to component and system reliability, their relationship, and problems of inference. Topics include component lifetime distributions and hazard functions, parameter estimation and hypothesis testing, life testing, accelerated life testing, system structural functions, and system maintainability. ir

682/OR 682/MATH 685/CSI 700 Computational Methods in Engineering and Statistics (3:3:0). Prerequisites: MATH 203 and 213 or equivalent or permission of instructor. Numerical methods have been developed to solve mathematical problems that lack explicit closed-form solutions or have solutions that are not amenable to computer calculations. Examples include solving differential equations or computing probabilities. Discusses numerical methods for such problems as regression, analysis of variance, nonlinear equations, differential and difference equations, and nonlinear optimization. Applications in statistics and engineering are emphasized. s

700/ HSCI 800 Advanced Quantitative Data Analysis for Healthcare Research II (3:3:0). Prerequisite: STAT 535 or HSCI 799. Multivariate analysis of variance (MANOVA, MANCOVA), multiple regression, and logistical regression. Students learn how to intelligently apply multivariate statistical methods to data, to carry out the necessary computations using statistical software, and to correctly interpret the results and make accurate statements about their findings. Cannot be used to satisfy the requirements of the MS in Statistical Science degree. ir

701/HSCI 801 Advanced Multivariate Statistics and Data Analysis for Healthcare Research (3:3:0). Prerequisites: STAT 700/HSCI 800 or equivalent. Coverage of discriminate analysis, canonical correlation analysis, structural analysis (LISREL and path analysis), and factor analysis. Cannot be used to satisfy the requirements of the MS in Statistical Science degree. ir

719/OR 719/CSI 775 Computational Models of Probabilistic Reasoning (3:3:0). Prerequisites: STAT 652 or 664, or permission of instructor. Introduction to theory and methods for building computationally efficient software agents that reason, act, and learn environments characterized by noisy and uncertain information. Covers methods based on graphical probability and decision models. Students study approaches to representing knowledge about uncertain phenomena, and planning and acting under uncertainty. Topics include knowledge engineering, exact and approximate inference in graphical models, learning in graphical models, temporal reasoning, planning, and decision-making. Practical model building experience is provided. Students apply what they learn to a semester-long project of their own choosing.

751/CSI 771 Computational Statistics (3:3:0). Prerequisites: STAT 544, 554, and 652. Study of the basic computational-intensive statistical methods and related methods that would not be feasible without modern computational resources. Covers nonparametric density estimation including kernel methods, orthogonal series methods and multivariate methods, recursive methods, cross-validation, nonparametric regression, penalized smoothing splines, the jackknife and bootstrapping, computational aspects of exploratory methods including the grand tour, projection pursuit, alternating conditional expectations, and inverse regression methods. af

753 Computer Intrusion Detection (3:3:0). Prerequisite: STAT 554 or STAT 663 or permission of instructor. A statistical approach to computer intrusion detection. Networking basics, TCP/IP networking, network statistics, evaluation, intrusion detection, network monitoring, host monitoring, computer viruses and worms, Trojan programs and covert channels. s

779 Topics in Survey Design and Analysis (1-3:1-3:0). Prerequisite: STAT 674 or permission of instructor. Specialized advanced topics in survey sampling building on the foundations in STAT 574 and 674. Topics offered will vary according to the interest and availability of instructors. They include, but are not limited to, administrative records in the analysis of data, adaptive sampling, calibration estimators, capture-recapture models, data security, establishment surveys, model-based inference, measurement error models, non-response models, imputation, multivariate analysis of survey data, record linkage, small area estimation, spatial sampling, survey errors and costs, telephone survey methods, variance estimation, web-based survey methods. Topics may be offered in the form of modules from one to three credits, with a one-credit module being offered over a period of five weeks. Up to three modules may be offered in a single semester for a total of one to three credits. Students may earn up to six credits in this course under different topics. ir

781/SYST 781/INFS 781 Data Mining and Knowledge Discovery (3:3:0). Prerequisite: STAT 663/CSI 773 or STAT 554 or CS 580 or STAT664/SYST 664 or CS 650 or INFS 614 or 623 or permission of instructor. Concerned with statistical and computational methods and systems for deriving user-oriented knowledge from large databases and other information sources, and applying this knowledge to support decision making. Information sources can be in numerical, textual, visual, or multimedia forms. Covers theoretical and practical aspects of current methods and selected systems for data mining, knowledge discovery, and knowledge management, including those for text mining, multimedia mining and web mining. Content may vary from semester to semester.

789 Advanced Topics in Statistics (1-6:1-6:0). Prerequisite: Permission of instructor. Topics in statistics not covered in the regular statistics sequence. May be repeated for credit. ir

798 Master's Essay (3:0:0). Prerequisites: Nine graduate credits and permission of instructor. Project chosen and completed under the guidance of a graduate faculty member, that results in an acceptable technical report.

799 Master's Thesis (1-6:0:0). Prerequisites: Nine graduate credits and permission of instructor. Project chosen and completed under the guidance of a graduate faculty member, that results in an acceptable technical report and oral defense.