Statistics (STAT)

Related Catalog Entry: School of Information Technology and Engineering / Statistics

Related Mason Website: School of Information Technology and Engineering (http://ite.gmu.edu/)

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.

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.

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.

362 Introduction to Computer Statistical Packages (3:3:0). Prerequisite: STAT 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,s

455 Experimental Design (3:3:0). Prerequisite: STAT 350, 354, or DESC 353. 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.

457 Applied Nonparametric Statistics (3:3:0). Prerequisites: STAT 350, STAT 354, DESC 353, 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.

463 Introduction to Exploratory Data Analysis (3:3:0). Prerequisite: STAT 250 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.

474 Introduction to Survey Sampling (3:3:0). Prerequisite: 300-level course in probability or statistics. 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: 60undergraduate 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.

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 theory, distributions, sampling, inference, estimation and hypothesis testing; linear regression and correlation; and the analysis of variance. Credits are not applicable toward the M.S. in Operations Research and Management Science or in Statistical Science.

512 The Use of Computer Statistical Packages (3:3:0). Prerequisites: CS 103 or equivalent and a course in statistics, or permission of instructor. Credits are not applicable toward the credit requirements for the M.S. in Mathematics, Computer Science, Operations Research and Management Science, or Statistical Science, but may be applicable toward a degree in some other fields. Introduction to use of computer packages in the statistical analysis of data. Techniques common to use of all statistical packages, including data checking, cleaning, manipulation, and transformation, are emphasized. Both simple and complex statistical analyses are covered. Techniques are illustrated by concentrating on one of the major statistical packages such as SAS or SPSS. Other packages are discussed and compared. Students are expected to perform computer statistical analyses of data relevant to their respective fields of study.

530 Mathematical Methods for Statistics and Engineering (3:3:0). Prerequisite: MATH 108 or 113. Calculus, linear algebra, and probability results required for the pursuit of an advanced degree in statistics or a related field. 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. f,s

574 Survey Sampling I (3:3:0). Prerequisite: STAT 354 or 554. 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 may be required. f

634 Case Studies in Data Analysis (3:3:0). Prerequisite: STAT 554 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.

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 hypothesis, and likelihood ratio tests. s

655 Analysis of Variance (3:3:0). Prerequisite: STAT 554 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. af

656 Regression Analysis (3:3:0). Prerequisites: STAT 554 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. s

657 Nonparametric Statistics (3:3:0). Prerequisite: STAT 554 or 652 or equivalent. 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, auto regressive, moving average and mixed model processes, hidden periodicity models, properties of models, autocovariance functions, auto correlation functions, partial auto correlation functions, spectral density functions, identification of models, estimation of model parameters, and forecasting techniques.

662 Multivariate Statistical Methods (3:3:0). Prerequisite: STAT 554 or equivalent. 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 co variance, 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. af

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.

664/SYST 664 Bayesian Inference and Decision Analysis (3:3:0). Prerequisite: STAT 544 or 554 or equivalent, or permission of instructor. Fundamentals of Bayesian decision theory and its application in statistical inference and decision analysis. Topics include prior distributions and Bayes theorem, proper scoring rules, conjugate priors, approximate posterior distributions, multiattribute utility theory, influence diagrams and Bayesian networks, measuring utilities, and probability distributions. s

665 Categorical Data Analysis (3:3:0). Prerequisite: STAT 554 or equivalent. 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 analysis of incomplete tables. A computer statistical package is used extensively for data analysis. as

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. af

674 Survey Sampling II (3:3:0). Prerequisites: STAT 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. s

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.

679 Topics in Survey Design and Analysis (3:3:0). Prerequisite: STAT 674 or permission of instructor. Seminar format in which topics are presented according to the interests of students and instructors. Topics may include use of administrative records in analysis of survey data, adaptive sampling, capture-recapture sampling to estimate population size, telephone survey methods, establishment surveys, survey errors and costs, imputation methods for item nonresponse, small area estimation, technique of inter penetrating samples, variance estimation, model versus design-based inference, randomized response for sensitive questions, multivariate analysis of survey data, and spatial sampling.

682/OR 682/MATH 685/CSI 700 Computational Methods in Engineering and Statistics (3:3:0). Prerequisites: MATH 203 and MATH 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 Multivariate Statistics and Data Analysis I (4:3:1). Prerequisites: STAT 510 or equivalent. Coverage of regression (simple, multiple, multivariate), two-sample tests of means, analysis of variance (ANOVA, ANCOVA, MANOVA, MANCOVA, factorial designs, repeated measures), and factor analysis exploratory and confirmatory), with an emphasis on applications in the health and biological science. 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 M.S. in Statistical Science degree.

701 Multivariate Statistics and Data Analysis II (3:0:0). Prerequisites: STAT 700, HSCI 800 or equivalent. Coverage of discriminate analysis, canonical correlation analysis, structural analysis (LISREL and path analysis), confirmatory factor analysis, and other selected topics (e.g., principal component analysis, cluster analysis, multidimensional scaling, classification trees, etc., depending upon the interests of the class), with an emphasis on applications in the health and biological sciences. 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 M.S. in Statistical Science degree.

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 boot strapping, computational aspects of exploratory methods including the grand tour, projection pursuit, alternating conditional expectations, and inverse regression methods.

774 Statistical Inference for Survey Sampling (3:3:0). Prerequisite: STAT 674. Variance estimation using re sampling methods such as balanced half-samples, jackknife and bootstraps methods, inference for percentiles, model-based inference under super populations, and Bayesian methods. af

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 STAT 664/SYST 664 or CS 650 or INFS 614 or INFS 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). PPre requisite: Permission of instructor. Topics in statistics not covered in the regular statistics sequence. May be repeated for credit.

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.