# Statistics (STAT)

## Statistics

250 Introductory Statistics I (3:3:0) Prerequisite: high school algebra. Elementary introduction to statistics. Topics include descriptive statistics, probability, and estimation and hypothesis testing for means and proportions. Statistical software used 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. f,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 or equivalent. Use of computer packages in statistical analysis of data. Topics include data entry, checking, and manipulation; and use of computer statistical packages for regression and analysis of variance. s

435 Analysis of Experimental Data Using SPSS (3:3:0) Prerequisite: STAT 250 or equivalent. Statistical methods for analysis of experimental data, including ANOVA and regression. Parametric and nonparametric inference methods appropriate for a variety of experimental designs are presented along with data analysis using SPSS. Intended primarily for researchers in the natural, social, and life sciences. f

455 Experimental Design (3:3:0) Prerequisites: 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; and design of experiments, including factorial, hierarchical, and split plot designs. Optional topics may include analysis of covariance; partial hierarchical designs; incomplete block designs; principles of blocking and confounding in 2**n experiments; or estimation of variance components. Computer statistical packages are used to perform computations. ir

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. ir

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. ir

474 Introduction to Survey Sampling (3:3:0) Prerequisite: STAT 350 or 354 and STAT 362 or permission of instructor. Introduction to design and analysis of sample surveys. Sample designs 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 applied to case studies of actual surveys. Class project may be required. 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 maximum 6 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 nature of topic. Topics of special interest to undergraduates. May be repeated for maximum 6 credits if topics substantially differ.

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

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 department. Topics include 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 501–503 can be applied to certificate programs in statistics. s

503 SAS Macro Language (1:1:0) Prerequisite: STAT 501. Introduction to SAS Macro Language. Continued preparation beyond STAT 501 for graduate students in use of SAS for other graduate courses offered by department. Topics include 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 501–503 can be applied to certificate programs in statistics. s

535 Analysis of Experimental Data Using SPSS (3:3:0) Prerequisite: STAT 250 or equivalent. Statistical methods for analysis of experimental data, including ANOVA and regression. Parametric and nonparametric inference methods appropriate for a variety of experimental designs are presented along with data analysis using SPSS. Intended primarily for researchers in the natural, social, and life sciences. Can be used to satisfy requirements for certificates in federal statistics and biostatistics, but not MS in statistical science. Certificate program students granted credit for only one of STAT 535 or 554. f

544 Applied Probability (3:3:0) Prerequisite: Math 213 and STAT 344, or permission of instructor. Course in probability with applications in computer science, engineering, operations research, and statistics. Random variables and expectation, multivariate and conditional distributions, conditional expectation, order statistics, transformations, moment generating functions, special distributions, limit theorems. 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. Certificate program students granted credit for only one of STAT 535 or 554. f,s

574 Survey Sampling I (3:3:0) Prerequisite: STAT 354 or 554; corequisite: STAT 362 or permission of instructor. 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. Discusses practical problems in conducting a survey. Methods applied to case studies of actual surveys. Class project 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. ir

645/OR 645 Stochastic Processes (3:3:0) Prerequisite: OR 542 or 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 on applications in practice, as well as analytical models.

652/CSI 672 Statistical Inference (3:3:0) Prerequisite: STAT 544, 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 501, or 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, STAT 501, and matrix algebra; or permission of instructor. 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 544 and 554. Distribution-free procedures for making inferences about one or more samples. Tests for lack of independence, association or trend, and 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/CSI 678 Time Series Analysis and Forecasting (3:3:0) Prerequisite: STAT 544 or equivalent. Modeling stationary and nonstationary processes, autoregressive, moving average and mixed model processes, autocovariance functions, autocorrelation functions, partial autocorrelation functions, spectral density functions, identification of models, estimation of model parameters, and forecasting techniques. af

660 Biostatistical Methods (3:3:0) Prerequisites: STAT 554 or STAT 535 and a working knowledge of a statistical software package, such as SAS or SPSS. Focuses on biostatistical aspects of design and analysis of biomedical studies, including epidemiologic observational studies and randomized clinical trials. Topics include randomization principle, confounding, ethics in human experimentation, methods of randomization, stratification, primary outcome analyses, covariate-adjusted analyses, epidemiologic measures, and sample size and power computation. s

662 Multivariate Statistical Methods (3:3:0) Prerequisites: STAT 554 or equivalent, and STAT 501; or permission of instructor. Standard techniques of applied multivariate analysis. Topics include review of matrices, T square 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 is 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 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, 554, or equivalent. Introduces decision theory and relationship to Bayesian statistical inference. Teaches commonalities, differences between 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. Teaches necessary theory to develop firm understanding of when and how to apply Bayesian and frequentist methods, and practical procedures for inference, hypothesis testing, and developing statistical models for phenomena. Teaches fundamentals of Bayesian theory of inference, including probability as a representation for degrees of belief, likelihood principle, use of Bayes Rule to revise beliefs based on evidence, conjugate prior distributions for common statistical models, and methods for approximating the posterior distribution. Introduces graphical models for constructing complex probability and decision models from modular components. s

665 Categorical Data Analysis (3:3:0) Prerequisites: STAT 554 or equivalent, STAT 656, and STAT 501. Analyzes 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 association tests and measures of association in two- and three-dimensional contingency tables, logistic regression, and loglinear models. Computer statistical package used extensively for data analysis. as

668 Survival Analysis (3:3:0) Prerequisites: STAT 544, 554 or 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 factors affecting survival times of patients following treatment, usually in the setting of clinical trials. Methods can also be applied to the social and natural sciences and engineering where they are known by other names (reliability, event history analysis). 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 analysis of real data from major medical studies using SAS software. af

673 Statistical Methods for Longitudinal Data Analysis (3:3:0) Prerequisites: STAT 544, STAT 656, and working knowledge of a statistical software package. Presents modern statistical approaches to the analysis of longitudinal data, i.e., data collected repeatedly on experimental units over time (or other conditions). Topics include linear mixed effects models, generalized linear models for correlated data (including generalized estimating equations), and computational issues and methods for fitting models. as

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. as

677/OR 677/SYST 677 Statistical Process Control (3:3:0) Prerequisite: STAT 544 or 554, or permission of instructor. Introduces concepts of quality control and reliability. Acceptance sampling, control charts, and economic design of quality control systems are discussed, as are system reliability, fault-tree analysis, life testing, repairable systems, and the role of reliability, quality control, and maintainability in life-cycle costing. Role of MIL and ANSI standards in reliability and quality programs also considered.

678/OR 675 Reliability Analysis (3:3:0) Prerequisite: STAT 544 or 554, or permission of instructor. Introduces 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

700 Advanced Quantitative Data Analysis for Health Care Research II (3:3:0) Prerequisite: STAT 535 or HSCI 799. Multivariate analysis of variance (MANOVA, MANCOVA), multiple regression, and logistic regression. Students apply multivariate statistical methods using statistical software to analyze and interpret data in health care research. Cannot be used to satisfy requirements for MS in statistical science. ir

701 Advanced Multivariate Statistics and Data Analysis in Health Care 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 requirements for MS in statistical science. ir

719/OR 719/CSI 775 Computational Models of Probabilistic Reasoning (3:3:0) Prerequisites: STAT 652 or SYST/STAT 664, or permission of instructor. Introduces 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 semester-long project of their own choosing.

751/CSI 771 Computational Statistics (3:3:0) Prerequisites: STAT 544, STAT 554, and STAT 652. Covers basic computationally intensive statistical methods and related methods, which 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 663, or permission of instructor. 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. ir

758 Advanced Time Series Analysis (3:3:0) Prerequisite: STAT 658. Mathematical modeling and methods for model identification and forecasting of nonstationary and seasonal time series data (ARIMA models), multivariate time series, and state-space models. as

760 Advanced Biostatistical Methods (3:3:0) Prerequisites: STAT 544, STAT 652, working knowledge of statistical programming language. Advanced statistical methods in the drug development process. Provides the theoretical statistical basis for the design and analysis of pharmaceutical clinical trials. Topics include the theory of randomization, randomization-based inference, restricted, response-adaptive, and covariate-adaptive randomization, the modern theory of group sequential monitoring, statistical aspects of determination of dose-response relationships. af

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 foundations in STAT 574 and 674. Topics vary according to interest and availability of instructors, but may include administrative records in analysis of data, adaptive sampling, calibration estimators, capture-recapture models, data security, establishment surveys, model-based inference, measurement error models, nonresponse 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 form of modules from 1 to 3 credits, with 1-credit module offered over five weeks. Up to three modules may be offered in single semester for maximum 3 credits. Students may earn up to 6 credits under different topics. ir

781/SYST 781 Data Mining and Knowledge Discovery (3:3:0) Prerequisite: One of the following courses: CS 687, CS 650, INFS 614, STAT 663, STAT 664, or permission of instructor. Statistical and computational methods and systems for deriving user-oriented knowledge from large databases and other information sources, and applying 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 regular statistics sequence. May be repeated for credit. ir

796, 797 Directed Reading and Research (1-3:0:0) Prerequisite: admission to PhD program in Statistical Science. Reading and research on specific topic in statistics under direction of faculty member.

798 Master’s Essay (3:0:0) Prerequisites: 9 graduate credits, and permission of instructor. Project chosen and completed under guidance of graduate faculty member that results in acceptable technical report.

799 Master’s Thesis (1–6:0:0) Prerequisites: 9 graduate credits, and permission of instructor. Project chosen and completed under guidance of graduate faculty member that results in acceptable technical report and oral defense.

871/IT 871 Statistical Data Mining (3:3:0) Prerequisite: STAT 554 or 663, or permission of instructor. Covers basic concepts, computational complexity, data preparation and compression, databases and SQL, rule-based machine learning and probability, density estimation, exploratory data analysis, cluster analysis and pattern recognition, artificial neural networks, classification and regression trees, correlation and nonparametric regression, time series, and visual data mining. ir

875/IT 875/CSI 703 Scientific and Statistical Visualization (3:3:0) Prerequisite: CS 652, STAT 554, STAT 663, or STAT 751; or permission of instructor. Covers visualization methods used to provide new insights and intuition concerning measurements of natural phenomena, and scientific and mathematical models. Presents case studies from myriad disciplines. Topics include human perception and cognition, introduction to graphics laboratory, elements of graphing data, representation of space-time and vector variables, representation of three-dimensional and higher dimensional data, dynamic graphical methods, and virtual reality. Work on a visualization project required. Emphasizes software tools on Silicon Graphics workstation, but other workstations and software may be used. s

876/IT 876/CSI 876 Measure and Linear Spaces (3:3:0) Prerequisites: STAT 544 and MATH 315. Measure theory and integration; convergence theorems; theory of linear spaces and functional analysis; and probability theory. The theory of linear spaces includes normed linear spaces, inner product spaces, Banach and Hilbert spaces, Sobelev spaces, and reproducing kernels. Topics include wavelets, applications to stochastic processes, and nonparametric functional inference. f

877/IT 877/CSI 877 Geometric Methods in Statistics (3:3:0) Prerequisite: STAT 751 or permission of instructor. Develops foundations of geometric methods for statistics. Topics include n-dimension Euclidian geometry; projective geometry; differential geometry, including curves, surfaces, and n-dimensional differentiable manifolds; and computational geometry, including computation of convex hulls, tessellations of two-, three-, and n-dimensional spaces, and finite element grid generation. Examples include applications to scientific visualization. ir

971/IT 971 Probability Theory (3:3:0) Prerequisite: STAT 544 and MATH 315. A rigorous measure-theoretic treatment of probability. Includes expectation, distributions, laws of large numbers and central limit theorems for independent random variables, characteristic function methods, conditional expectations, martingales, strong and weak convergence, and Markov chains. s

972/IT 972/CSI 972 Mathematical Statistics I (3:3:0) Prerequisites: STAT 652/CSI 672 or equivalent, and either STAT 876/IT 876/CSI 876 or STAT 971/IT 971. Focuses on theory of estimation. Includes method of moments, least squares, maximum likelihood, and maximum entropy methods. Details methods of minimum variance unbiased estimation. Topics include sufficiency and completeness of statistics, Fisher information, Cramer-Rao bounds, Bhattacharyya bounds, asymptotic consistency and distributions, statistical decision theory, minimax and Bayesian decision rules, and applications to engineering and scientific problems. f

973/IT 973/CSI 973 Mathematical Statistics II (3:3:0) Prerequisite: STAT 972/IT 972/CSI 972. Continuation of STAT 972/IT 972/CSI 972. Concentrates on theory of hypothesis testing. Topics include characterizing decision process, simple versus simple hypothesis tests, Neyman-Pearson Lemma, uniformly most powerful tests, unbiasedness and invariance of tests, and randomized and sequential tests. Applications of testing principles made to situations in normal distribution family and other families of distributions. s

998 Doctoral Dissertation Proposal (1–12:0:0) Work on research proposal that forms basis for doctoral dissertation. May be repeated. No more than 24 credits of STAT 998 and 999 may be applied to doctoral degree requirements.

999 Doctoral Dissertation (1–12:0:0) Prerequisite: Admission to candidacy. Formal record of commitment to doctoral dissertation research under direction of faculty member in statistics. May be repeated as needed; no more than 24 credits of STAT 998 and 999 may be applied to doctoral degree requirements.