Virginia Tech™home

Graduate Courses

5014: Introduction to Statistical Program Packages

Introduction to managing, plotting, and analyzing data in R and SAS. Introduction to LaTex. Pass/Fail only.

Pre: Graduate standing in Department of Statistics. (1H,1C). I.

5024: Effective Communication in Statistical Consulting

Developing the communication skills necessary to be effective interdisciplinary statistical collaborators. Topics include explaining and presenting statistical concepts to a non-statistical audience, learning how to help scientists answer their research questions, and managing an effective statistical collaboration meeting.

Pre: Graduate standing in the Department of Statistics, 5014; Co: 5124, and 5204 (3H, 3C).

5034: Inference Fundamentals with Applications to Categorical Data

Fundamental ideas of statistical estimation and testing; principles and methods for standard one-sample and two-sample settings; applications to categorical data problems. Topics include point and interval estimation, including small and large sample procedures, the likelihood principle; hypothesis testing including exact and large-sample tests; nonparametric and resampling inference; one-way, two-way and multi-way analysis of variance.

Pre: Graduate standing, Department of Statistics, MATH/STAT 4584. Co: 5014. (3H, 3C).

5044: Regression and ANOVA

Principles and methods of data analysis employing linear models for both continuous response variables and categorical variables. Topics include both classical descriptive measures and modern computer-based techniques for data visualization; simple, polynomial, multiple and weighted regression; Box-Cox transformation; model diagnosis; variable selection; categorical data analysis; the generalized linear model.

Pre: Graduate standing, Department of Statistics, 5034, MATH/STAT 4584. Co: 5014. (3H,3C).

5104: Probability and Distribution Theory

Fundamental concepts of probability, random variables and their distributions, functions of random variables, mathematical expectations, and stochastic convergence.

Pre: MATH 4526; (3H,3C). I.

5114: Statistical Inference

Decision theoretic formulation of statistical inference, concept and methods of point and confidence set estimation, notion and theory of hypothesis testing, relation between confidence set estimation and hypothesis testing.

Co: 5104. (3H,3C). II.

5124: Linear Models Theory

The class covers matrix algebra including solving linear equation systems, distributions of linear combinations and quadratic forms involving normal random variables, and the fundamental aspects of the general linear model including the estimation, hypothesis testing and confidence interval procedures for multiple regression and analysis of variance. Theory on linear mixed models is also covered. The class covers matrix algebra including solving linear equation systems, distributions of linear combinations and quadratic forms involving normal random variables, and the fundamental aspects of the general linear model including the estimation, hypothesis testing and confidence interval procedures for multiple regression and analysis of variance. Theory on linear mixed models is also covered.

Pre: 5114 and MATH 5524; (3H,3C). II.

5204: Experimental Design and Analysis I

Principles and concepts of experimental design; systematic overview and discussion of basic designs from the point of view of blocking, error reduction, and treatment structure; and development of analysis based on linear models. Includes designs with one or more blocking factors, split-plot designs, repeated measures, fractional factorials, orthogonal arrays.

Pre: 5044, 5104; (3H,3C). II.

5204G: Experimental Design: Concepts and Applications

Fundamental principles of designing and analyzing experiments with application to problems in various subject matter areas. Discussion of completely randomized, randomized complete block, and Latin square designs, analysis of covariance, split--plot designs, factorial and fractional designs, incomplete block designs. Project required.

Pre: one of 3006, 3616, 4106, 4706, 5605, 5615. (3H,3C). I.

5214G: Advanced Methods of Regression Analysis

Multiple regression including variable selection procedures; detection and effects of multicollinearity; identification and effects of influential observations; residual analysis; use of transformations. Non-linear regression, the use of indicator variables, and logistic regression. Use of SAS.

Pre: STAT 5605 or STAT 5615.

5304: Statistical Computing

A comprehensive course in simulation based sampling methodology designed to develop an understanding of computational methods for statistics. Topics covered include Monte Carlo integration, importance sampling, Markov chain Monte Carlo, particle methods, Kalman filtering. Both theoretical and applied aspects will be emphasized.

Pre: 5034, 5044, (3H,3C).I. Alternate years.

5334: Exploratory and Robust Data Analysis

Analysis of data by graphical and numerical techniques, statistical analysis of non-Gaussian data, topics in robust estimation for location, regression and anova models via parametric and nonparametric methods, and Monte Carlo and bootstrap techniques.

Pre: 5114, (3H,3C). I. Alternate years.

5354: Structured Process Improvement

An introduction to the selection, management, leadership and execution of structured process improvement projects. Topics include effective roadmaps for process improvement, team facilitation and leadership, project selection and management, sampling, process capability analysis, data transformations, variance component analysis, response surface methodology (including full and fractional factorial designs, Plackett-Burman designs, central composite designs, Box-Behnken designs, analysis of variance, regression, and multi-response optimization), and statistical process control.

Pre: 5034,5044. (3H, 3C) I.

5364: Hierarchial Modeling

Hierarchial modeling techniques as applied to assess data with atypical features, such as non-normal responses (e.g., binary, discrete survival, continous mixtures), censored/missing observations, multivariate responses, repeated measures, and nested structures. Classical and Bayesian techniques for assessing models.

Programming experience in R, S+, or Matlab required.

5404: Nonparametric Statistics

Introduction to semiparametric and nonparametric regressions and methods to estimate these nonparametric functions. Estimation based regression splines and B-splines, penalized likelihood, and tests. Selected topics.

Pre: STAT 5114, STAT 5044, and STAT 5514.

5414: Time Series Analysis I

Analysis of serially dependent data -, including stationary and nonstationary time series, Box-Jenkins modeling, trend elimination, prediction, unit root testing, intervention analysis, transfer function models, and applications in economics and engineering.

Pre: 5114; (3H,3C). I. Alternate years.

5434: Applied Stochastic Processes

Stochastic processes in statistical applications including Markov chains, Poisson processes, renewal processes, branching processes, random walks, martingales, Brownian motion and related stationary Gaussian processes.

Pre: 5104. (3H, 3C). II.

5444: Bayesian Statistics

Introductory course of Bayesian statistics on basic concepts of probability, Bayesian inference of Normal, Binomial, Poisson, Uniform and other common distributions, selections of prior information, Bayesian decision theory, Bayesian analysis of regression and analysis of variance and Bayesian foundation.

Pre: 5114; (3H,3C). II. Even years.

5454: Reliability Theory

The objective of this course is to provide a comprehensive introduction to the principles and methods for the analysis of time-to-event data. Time-to-event data are common in biomedical and public health research, as well as in ecology, social science, and industrial research. This course will cover parametric, nonparametric, and semiparametric methods with focus on applications in biomedical/public health, and industrial settings. Topics include types of censoring and truncation; parametric lifetime distributions and likelihood construction; survival function estimation; nonparametric two or more samples tests; parametric inference, Cox semiparametric regression, accelerated life testing regression diagnostics; competing risks; frailty model.

Pre: STAT 5044, 5104, 5114 (or equivalent courses); 3H, 3C. I. Alternate years.

5464 (ISE 5464): Queuing Theory

Classic models of queues including M/M/1, M/GI/1, and GI/M/s. Topics in queue length processes, waiting time processes, busy period processes, and traffic processes.

Pre: STAT 5434 or ISE 5414; (3H,3C). I. Even years.

5474 (ISE 5474): Statistical Theory of Quality Control

Development of statistical concepts and theory underlying procedures used in quality control applications. Process improvement strategies, capability analysis, measurement system analysis, process monitoring with control charts, multivariate process monitoring, profile monitoring, health-related surveillance, Markov chains, use of basic time series models.

Pre: STAT 5104, 5114; (3H,3C). I. Alternate years.

5504: Multivariate Statistical Methods

Methods useful for description and inference for multivariate data. Multivariate distributions, location and dispersion problems for one and two samples, multivariate analysis of variance, linear models, repeated measurements, principal components, factor analysis, biplots, discriminant and canonical analysis, cluster analysis, multidimensional scaling and correspondence analysis. Uses SAS or R.

Pre: STAT 5124 (3H,3C). I. Even years.

5504G: Advanced Applied Multivariate Methods

Non-mathematical study of multivariate analysis. Multivariate analogs of uinivariate test and estimation procedures. Simultaneous inference procedures. Multivariate analysis of variance, repeated measures, inference for dispersion and association parameters, principle components analysis, discriminant analysis, cluster analysis.

Pre: STAT 5606 or STAT 5616. Graduate Standing required.

5514: Topics in Regression

Classical and modern techniques in regression analysis are discussed for linear, nonlinear, generalized linear models (including logistic and Poisson regression), and linear mixed models. Use of modern regression techniques to diagnose model performance. Diagnostics to detect unusual observations and collinearity. The study of biased estimation methods (including ridge and principal component regression) and numerical methods used in regression.

Pre: 5114, 5124; (3H,3C). I.

5524: Sample Survey Theory

Theory of sample surveys including major sampling designs, sample size determination, estimation and interval estimation, and questionnaire design.

Pre: 5034,5044; (3H,3C). I. Alternate years.

5524G: Advanced Sample Survey Methods

Statistical methods for the design and analysis of survey sampling. Fundamental survey designs. Methods of randomization specific to various survey designs. Estimation of population means, proportions, totals, variances, and mean squared errors. Design of questionnaires and organization of a survey are also covered. Project required.

Pre: One of 3006, 3616, 4106, 4706, 5606, 5616. (3H,3C). I. Odd years.

5525 (CS 5525): Data Analytics I

Basic principles of data mining, including data analysis under uncertainty, modeling of data mining problems, data mining algorithms, scalability, and data integration and management, Applications of data mining in areas such as bioinformatics, electronic commerce, and environmetrics.

Pre: 5034, 5044 or graduate standing in CS; (3H, 3C). I.

5526 (CS 5526): Data Analytics II

Advanced techniques in supervised, unsupervised, and visualized learning in high dimensional spaces. Methodology will be focused on theoretical, probabilistic, as well as applied aspects of data analytics. Methods will include generalized linear models in high dimensional spaces, regularization, lasso and related methods, principal component regression (pca), tree methods, and random forests. Clustering methods including K means, hierarchical clustering, biclustering, and model-based clustering will be examined. Distance-based learning methods such as multi dimensional scaling, the self organizing map, graphical/network models, and isomap will be demonstrated in conjunction with probabilistically based alternative methods. Supervised learning will consist of discriminant analyses, supervised pca, support vector machines, and kernel methods.

Pre: 5444, 5505. (3H, 3C), II.

5534: Analysis of Multivariate Categorical Data

Log-linear models for unconstrained and ordinal multidimensional contingency tables; testing and estimation; random and structural zeros; model building; logit models and logistic regression; and use of major statistical packages.

Pre: 5124; (3H,3C). I. Alternate years.

5544: Spatial Statistics

Spatial data structures: geostatistical data, lattices, and point patterns. Stationary and isotropic random fields. Autocorrelated data structures. Semivariogram estimation and spatial prediction for geostatistical data. Mapped and sampled point patterns. Regular, completely random, and clustered point processes. Spatial regression and neighborhood analyses for data on lattices.

Pre: 5124 (3H,3C). III. Even years.

5564: Statistical Genetics

Probabilistic approach to behavior of random mating populations, effects of inbreeding and elementary selection, population fitness, and natural selection. Statistical concepts in quantitative inheritance for random and non-random mating populations, correlation between relatives, and artificial selection.

Pre: 5034,5044 and BIOL 3004; (3H,3C). II. Alternate years.

5574: Response Surface Design and Analysis I

Use of response surface analysis to design and analyze industrial experiments. First and second order models. First and second order experimental designs. Use of model diagnostics for finding optimum operating conditions.

Pre: 5204; (3H,3C). I. Odd years.

5584 (AAEC 5584): Basic Topics in Econometrics

Introduction to the concepts and methods in application of econometric analysis to problems of economic research.

Pre: 4724; (3H,3C). II.

5594: Topics in Biostatistics

Course with variable content; specialized application of statistical theory and methodology to biological and medical sciences; topics may vary and can include functional data analysis, longitudinal data analysis, bioassay, epidemiology, and statistical ecology.

Pre: 5114; (3H,3C). III. Odd years.

Functional Data Analysis: Functional data generalize the traditional data concept in statistics to focus on non-Euclidean data such as curves, graphs, and objects. Techniques presented include tools for exploring functional data, smoothing approaches transforming discrete functional data to smooth functions, function estimation under shape constraints, registration of functional data, functional principal component analysis, functional canonical correlation analysis, functional linear models and dynamic modeling. Recent research findings are reviewed.

Longitudinal Data Analysis: Statistical techniques for analyzing longitudinal data (repeated measures) will be covered. The primary focus is on application of the various statistical models and methods include univariate and multivariate analysis of variance for repeated measures, random-effects models, covariance pattern models, generalized estimating equations (GEE) models, random-effects logistic regression models, and missing data in longitudinal studies. The use of statistical software is also illustrated. The underlying statistical theory of models for longitudinal data analysis, including derivation and estimation of model parameters, will also be covered.

5605-5606: Biometry

5605: Descriptive statistics, the normal distribution, estimation, hypothesis testing, simple linear regression, and one-way analysis of variance and the use of JMP® software (a product of SAS) with applications to the biological sciences.

5606: Experimental design, nested and factorial analysis of variance, linear regression and correlation, multiple regression, and the use of JMP® software (a product of SAS), with applications to the biological sciences.

5606: Pre: 5605 or 5615. (3H,3C). 5605: I; 5606: II.

5615-5616: Statistics in Research

5615: Concepts in statistical inference, including basic probability, estimation, and test of hypothesis, point and interval estimation and inferences; simple linear regression; one-way analysis of variance and categorical data analysis.

5616: Experimental designs: basic concepts; completely randomized designs; randomized complete block designs; balanced incomplete block designs; Latin square designs; factorial treatment designs; mixed effects designs; split-plot designs. Multiple linear regression: general formulation, estimation and inference, variable selection, and model diagnostics.

Pre: 5615: 1 year calculus; 5616: 5615(3H,3C). 5615: I 5616: II.

5664: Applied Statistical Time Series Analysis for Reseach Scientists

Applied course in time series analysis methods. Topics include regression analysis, detecting andaddressing autocorrelation, modeling seasonal or cyclical trends, creating stationary time series, smoothing techniques, forecasting errors, and fitting autoregressive integrated moving average models.

Pre: 5616 or equivalent. 3H, 3C.II

5674: Methods in Biostatistics

Understanding the basis of descriptive and inferential methods applied in the biological and medical sciences. Topics include graphical and numerical exploratory data analysis, basic probability concepts and important probability distribution, sampling distribution, basic statistical inference methods including estimation, hypothesis testing, linear regression and analysis of variance. Additional topics include Chi-Square test, relative risk and odds ratio, and some basic nonparametric statistics. Student will learn to use JMP statistical software to calculate and graph descriptive statistics, and to perform the calculations of statistical inference.

5684: Survival Analysis

Models and methods for time-to-event data with focus on biological and biomedical applications. Topics includes types of censoring and truncation; likelihood construction; survival function estimation; nonparametric two or more samples tests; Cox semiparametric regression, time-dependent covariates; regression diagnostics; competing risks; frailty model.

Pre: STAT 5044, 5104, 5114 (or equivalent courses); 3H, 3C. I.

5694: Longitudinal Data Analysis

Application and theory for longitudinal data analysis for both continuous and categorical response data, including the use of statistical software for data analysis. Topics include ANOVA, MANOVA, random-effects model, convariance pattern models, generalized estimation equations models, random-effects logistic regression models, and missing data in longitudinal studies.

Pre: STAT 5044, 5104, 5114 (or equivalent courses); 3H, 3C. I.

5754: Internship in Statistics

A variable credit (from 1 to 3 hours) course, to be taken by statistics students who intern at an appropriate company or government agency performing statistical analysis under supervision of a corporate, or government, affiliate faculty member.

Pre: Graduate student stand in the Department of Statistics. Variable credit course. I, II, III, IV, V.

5894: Final Examination

Pass/fail only. (3H,3C).

5904: Project and Report

Internship in Statistics. Variable credit course. I,II,III,IV,V.

5924: Graduate Seminar

Special topics in statistical theory and applications. May be taken for credit two times (max. 2C). Pass/Fail only.

Pre: Graduate standing; (1H,1C). I,II.

5974: Independent Study

Pass/fail only. Variable credit course.

5984: Special Study

Special topics in statistics. Topics vary by semester. Including topics in environmetrics, ethics and the law, highly computational methods, Markov Chain Monte Carlo, mixed linear and nonlinear models. Variable credit course.

5984G: Statistical Genomics

Statistical methods for bioinformatics and genetic studies, with an emphasis on statistical analysis, assumptions and problem-solving. Topics include: basic concepts of genes and genomes, commonly used statistical methods for gene identification, association mapping and other related problems. Project required. Software: R.

Pre: graduate standing, STAT 5616 or equivalent (3H, 3C).

5994: Research and Thesis

Variable credit course.

6105: Measure and Probability

Sigma algebra; construction of probability measure and space; independent events; general measure and measurability; integral and Lp spaces; convergence of random variables.

Pre: STAT 5104 (3H, 3C), I.

6114: Advanced Topics in Statistical Inference

Advanced course in the theory of inference for graduate students in statistics and other qualified graduate students. Develops foundations, sufficiency, information, estimation, hypothesis testing, asymptotics, and unbiasedness.

Pre: 5114; (3H,3C). II.

6124: Stochastic Modeling and Inference

Data analyses and inferential techniques applied to data described by stochastic processes. Emphasize inferential techniques for Markov models, Poisson processes, point processes, birth/death processes, and cluster processes. Techniques for inference will apply to both stationary and nonstationary processes. Relationships between deterministic partial differential equation models and stochastic models will be examined. Modeling applications in time series, spatial analyses, genetics, epidemiology, text mining, and other application areas will be discussed.

Pre: 5434 (3H, 3C). II.

6404: Advanced Topics in Nonparametric Statistics

Topics of current interest in research for nonparametric theory and methods, using recent advanced texts and journal articles.

Pre: 5404, 6114; (3H,3C). II. Odd years. Alternate years.

6414: Time Series Analysis II

Weakly and strictly stationary stochastic processes; ergodic and ensemble theory; time and frequency domain; spectral decomposition theory; Hilbert space geometry; and multivariate spectra.

Pre: 5414; (3H,3C). II. Alternate years.

6424: Multivariate Statistical Analysis

Foundations of multivariate analysis. Distribution theory of vectors and matrices, inequalities, limit theory, the structure of some multivariate location-scale parameter families, derived distributions, invariant distributions, the principle of invariance in estimation and testing for multivariate location and scale parameters, and robust aspects of normal-theory multivariate procedures.

Pre: 5504; (3H,3C). II. Odd years.

6464 (ISE 6464): Queuing Networks

Applications of queuing theory results to queuing networks. Topics include reversibility, insensitivity, product forms for queue length processes, and traffic processes including traffic flow within the network.

Pre: ISE 5644, 6504; (3H,3C).

6474: Advanced Topics in Bayesian Statistics

This course introduces advanced Bayesian computing and methods and demonstrates their usefulness in challenging applied settings. Topics include Bayesian computing; model selection and criterion; nonparametric priors; semiparametric/nonparametric Bayesian approaches for random effects and survival analysis.

Pre: STAT 5114; 5124; 5514; 5444.

6484 (ISE 6484): Seminar in Applied Probability

Working seminar open to anyone doing research in applied probability. The purpose is to review student research progress through a series of seminars offered by them and to present new research results offered by faculty attending. May be taken more than once.

Pre: Enrollment in Ph.D. program; (1H,1C). I,II.

6494: Advanced Topics in Mathematical Statistics

Advanced treatment beyond standard course offerings in topics such as theory of inference, nonparametrics, sequential analysis, and limit theory. May be repeated for credit with different topics.

Pre: 5114 and consent; (3H,3C). II.

6504: Experimental Design and Analysis II

Theoretical treatment of optimality and construction of various types of designs, selected from incomplete block designs, fractional factorials, split-plot designs, regression designs, computer experiment designs, and others according to class interest.

Pre: 5124, 5204; (3H,3C). I. Alternate years.

6514: Advanced Topics in Regression

Advanced subjects in modern regression techniques and diagnostics. Advanced study of nonlinear models, generalized linear models, generalized estimating equations, nonparametric regression, mixed linear, finite mixture models, and measurement error model.

Pre: 5124 and 5514; (3H,3C). II. Even years.

6574: Response Surface Design and Analysis II

Advanced techniques and theory in response surface analysis and design. Robustness of designs. Thorough study of the notion of rotatability. Optimal design criteria and designs for estimating slopes of response surfaces. Mixture designs. Study of model misspecification.

Pre: 5574; (3H,3C). II. Odd years.

6584 (AAEC 6584): Advanced Topics in Econometrics

Advanced topics in the theory of econometrics, and the uses of advanced techniques in application to empirical problems.

Pre: 5584; (3H,3C). I.

6634 (EDRE 6634): Advanced Statistics for Education

Multiple regression procedures for analyzing data as applied in educational settings, including curvilinear regressions, dummy variables, multicollinearity, and introduction to path analysis.

Pre: STAT 5634; (3H,3C). II.

6644 (EDRE 6644): Advanced Research Design and Methodology

Principles of experimental design with applications to the behavioral sciences emphasizing appropriate statistical analysis.

Pre: STAT 5634; (3H,3C).

7994: Research and Dissertation

Variable credit course.