Department of Statistics

Kerchof Hall
University of Virginia
P.O. Box 400135
Charlottesville, VA 22904-4135
(434) 924-3222 Fax: (434) 924-3076
kwd2n@virginia.edu
www.stat.virginia.edu

Degree Requirements

Programs of Study The Department of Statistics administers programs leading to the degrees of Master of Science and Doctor of Philosophy. These programs provide diverse opportunities for advanced study and research in all areas of applied and theoretical statistics, and practical experience in statistical consulting.

The Master of Science (M.S.) degree is completed within three semesters, though in some cases, the degree can be completed in one calendar year (two semesters and a summer session). Candidates for the M.S. degree complete course requirements covering the breadth of applied and theoretical statistics, and statistical consulting, and pass certain general examinations based on those courses.

The Doctor of Philosophy (Ph.D.) degree is normally completed within five years. Candidates for the Ph.D. degree fulfill certain course requirements and examinations beyond the M.S. degree. The fundamental addition is the Ph.D. dissertation, which presents original research performed under the supervision of a faculty member.

All full-time graduate students are required, as part of their training, to gain instructional experience by assisting with the teaching of undergraduate courses.

Master of Science Degree

Course requirements The M.S. program requires 24 units of coursework. M.S. required courses: STAT 501, STAT 512, STAT 513, HES 704 or STAT995 and one of STAT 516, 531, or 718. The following courses will not count towards the required 24 units: STAT 997/STAT 999, STAT 598, STAT 912, MATH 311/509, MATH 312/510. STAT 501 may be taken S/NS; all other courses must be taken for a grade.

(For detailed course information, see statistical course offerings). Consulting (STAT 995) cannot be taken in the first semester of the M.S. program. In addition, a student may choose consulting as at most one of the three electives. No more than three units of consulting can be taken in any one semester and no more than 6 units are allowed overall.

Students are not permitted to register for Non-Topical Research. If a student registers for three courses, such a student needs to fill out a 12 unit program, and does so, by enrolling in STAT 912 (Statistics Seminar) for 3 units; a grade of S or NS will be given for STAT 912 based upon attendance. The credits for STAT 912, however, as noted above, do not count toward the 24 units requirement.

Examination Schedule There are two examinations required for the M.S. degree:

Master’s Exam This exam covers STAT 512, STAT 513, and either STAT 516, 531, or STAT 718; it is given once a year on the second Saturday in April (if this coincides with the Easter weekend, then it will be given on the third Saturday in April).

Language Exam This covers one programming language (SPlus) and one statistical package (SAS); it is given once a year on the second Saturday in April (if this coincides with the Easter weekend, then it will be given on the third Saturday in April).

Doctor of Philosophy Degree

Course requirements The Ph.D. degree requires 72 credits of statistics and approved mathematics courses at the 500 level and above. All statistics courses at the 500 level and higher, except STAT 501 and 520, may be counted toward the Ph.D. degree. Statistical consulting (STAT 995) is limited to a minimum of 3 and a maximum of 6 credits. Further, statistics seminar (STAT 912), directed reading (STAT 996), and non-topical or dissertation research (STAT 997 and 999) are limited to a combined total of 18 credits.

MATH 511, 531, 532, 551, 552, 731, 732 and 736 may be counted without special permission. MATH 510 or 512 may not be used toward the Ph.D. degree requirements. Other mathematics courses, as well as courses from other University programs, such as applied mathematics, computer science, economics, and systems engineering, may be counted subject to successful petition to the Graduate Committee of the Division of Statistics.

General examinations All students are required to take the Ph.D. General Exams at the end of the first year. The exams encompass the six required first year courses (Option A students take exams on five required first year courses). The exams are given on the Friday and Saturday preceding the first day of classes in the Fall semester of the second year. Only one retake is allowed; it is given on the Friday and Saturday preceding the first day of classes in Spring semester of the second year.

Qualifying examination The Ph.D. Qualifying Exam is designed to establish the candidate’s preparedness for dissertation research. It must be taken in the third year of graduate study. By the time of taking the examination, the candidate should have chosen a broad area of potential research (e.g. multivariate statistics) and a probable dissertation advisor. The Ph.D. Qualifying Exam is not intended as a dissertation proposal and it is not expected that the student have formulated a probable dissertation topic prior to taking the qualifying exam.

In consultation with the dissertation advisor, the student shall choose a committee of at least two faculty members. Normally this committee shall be chosen from the Statistics and Biostatistics faculty. The committee together with the student shall choose a small coherent package of one to three papers for the student to prepare and present. The selected papers should be in the student’s proposed area of dissertation research and should involve substantial statistical issues.

The format of the exam consists of a talk prepared by the student and delivered to the Statistics and Biostatistics graduate students and faculty. After the talk, the Statistics and Biostatistics faculty will question the student to establish the student’s understanding of the papers and of the background subject fields inherent in these papers.

Language requirement The Computer Language Exam covers one statistical programming language (S-Plus) and one statistical package (SAS); it is given once a year on the second Saturday in April (if this coincides with the Easter weekend, then it will be given on the third Saturday in April).

Course Descriptions

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STAT 500 - (3) (Y)
Introduction to Applied Statistics
Prerequisite: Instructor permission.
An introduction to estimation and hypothesis testing in applied statistics, especially the medical sciences. Measurement issues, measures of central tendency and dispersion, probability, discrete probability distributions (binomial and Poisson), continuous probability distributions (normal, t, chi-square, and F), and one- and two-sample inference, power and sample size calculations, introduction to non-parametric methods, one-way ANOVA and multiple comparisons. Students must also enroll in STAT 598 for 1 unit.

STAT 512 - (3) (Y)
Applied Linear Models
Prerequisite: MATH 312 or 510, or instructor permission; corequisite: STAT 598.
Linear regression models, inferences in regression analysis, model validation, selection of independent variables, multicollinearity, influential observations, autocorrelation in time series data, polynomial regression, and nonlinear regression.

STAT 513 - (3) (Y)
Applied Multivariate Statistics
Prerequisite: MATH 351 and 312 or 510, or instructor permission; corequisite: STAT 598.
Matrix algebra, random sampling, multivariate normal distributions, multivariate regression, MANOVA, principal components, factor analysis, discriminant analysis. Statistical software, such as SAS or S-PLUS, will be utilized.

STAT 514 - (3) (SI)
Survival Analysis and Reliability Theory
Prerequisite: MATH 312 or 510, or instructor permission; corequisite: STAT 598.
Lifetime distributions, hazard functions, competing-risks, proportional hazards, censored data, accelerated-life models, Kaplan-Meier estimator, stochastic models, renewal processes, Bayesian methods for lifetime, and reliability data analysis.

STAT 516 - (3) (E)
Experimental Design
Prerequisite: MATH 312 or 510, or instructor permission; corequisite: STAT 598.
Introduction to the basic concepts in experimental design, analysis of variance, multiple comparison tests, completely randomized design, general linear model approach to ANOVA, randomized block designs, Latin square and related designs, completely randomized factorial design with two or more treatments, hierarchical designs, split-plot and confounded factorial designs, and analysis of covariance.

STAT 517 - (3) (O)
Applied Time Series
Prerequisite: MATH 312 or 510, or instructor permission; corequisite: STAT 598.
The basic time series models in both the time domain (ARMA models) and the frequency domain (spectral models), emphasizing application to real data sets.

STAT 518 - (3) (SI)
Numerical Methods in Statistics
Prerequisite: MATH 351 and knowledge of a programming language suitable for scientific computation, or instructor permission.
Studies linear algebra and related numerical algorithms important to statistics, including linear least-squares, eigenvalues and eigenvectors, QR decomposition, singular value decomposition, and generalized matrix inverses.

STAT 519 - (3) (Y)
Introduction to Mathematical Statistics
Prerequisite: MATH 312 or 510, or instructor permission.
Studies statistical distribution theory, moments, transformations of random variables, point estimation, hypothesis testing, and confidence regions.

STAT 520 - (3) (E)
Design and Analysis of Sample Surveys
Prerequisite: STAT 110 or 112, or MATH 312, or instructor permission.
Discussion of the main designs and estimation techniques used in sample surveys: simple random sampling, stratification, cluster sampling, double sampling, post-stratification, ratio estimation. Nonresponse problems and measurement errors will also be discussed. Many properties of sample surveys will be developed through simulation procedures. The SUDAAN software package for analyzing sample surveys will be used. This course may not be used for graduate degrees in the Department of Statistics.

STAT 531 - (3) (Y)
Clinical Trials Methodology
Prerequisite: A basic statistics course (MATH 312/510) or instructor permission.
Studies experimental designs for randomized clinical trials, sources of bias in clinical studies, informed consent, logistics, and interim monitoring procedures (group sequential and Bayesian methods).

STAT 540 - (3) (SI)
Actuarial Statistics
Prerequisite: MATH 312 or 510, or instructor permission.
The course will cover the main topics required by students preparing for the examinations in Actuarial Statistics, set by the Society of Actuaries. Such topics include: life tables, life insurance and annuities, survival distributions, net premiums and premium reserves, multiple life functions and decrement models, valuation of pension plans, insurance models, benefits and dividends.

STAT 541 - (3) (SI)
Actuarial Risk Theory
Prerequisite: MATH 311 or APMA 310, or instructor permission.
In this course, the basics for actuarial risk theory are developed. It begins with the economics of insurance, and, using utility theory, shows why a risk averse individual would purchase insurance. Insurance models are presented and applied to calculate the probability of ruin, as a function cash reserves, the portfolio of policies, etc. Both individual risk theory (classical) and collective (modern) risk theory are fully discussed. The necessary probabilistic and statistical tools are developed within the course. The material covered is that required for the Society of Actuaries (SOA) Exam 151: Actuarial Risk Theory.

STAT 598 - (1) (S)
Applied Statistics Laboratory
Corequisite: 500-level STAT applied statistics course.
This laboratory component of the Department’s applied statistics program deals with the use of computer packages in data analysis. Enrollment in STAT 598 is required for all students in the Department’s 500-level applied statistics courses (STAT 512, 513, 514, 516, 517). STAT 598 may be taken repeatedly provided that a student is enrolled in at least one of these 500-level applied courses. However, no more than one unit of STAT 598 may be taken in any semester.

STAT 711 - (3) (Y)
Foundations of Statistics
Prerequisite: STAT 519 or instructor permission.
Introduction to the concepts of statistics via the establishment of fundamental principles which are then applied to practical problems. Such statistical principles as those of sufficiency, ancillarity, conditionality, and likelihood will be discussed.

STAT 712 - (3) (E)
Statistical Inference
Prerequisite: STAT 711 or instructor permission.
A rigorous mathematical development of the principles of statistics. Covers point and interval estimation, hypothesis testing, asymtotic theory, Bayesian statistics, and decision theory from a unified perspective.

STAT 713 - (3) (Y)
Generalized Linear Models
Prerequisite: STAT 512 and 519, or instructor permission.
Includes the origins of generalized linear models, classical linear models, probit analysis, logit models for proportions, log-linear models for counts, inverse polynomial models, binary data, polytomous data, quasi-likelihood models, and models for survival data.

STAT 714 - (3) (O)
Multivariate Statistical Analysis
Prerequisite: STAT 513 and 519, or instructor permission.
Includes multivariate normal distributions, maximum likelihood inference, invariance theory, sample correlation coefficients, Hotelling’s T2 statistic, Wishart distributions, discriminant analysis, and MANOVA.

STAT 715 - (3) (E)
Non-Parametric Statistical Analysis
Prerequisite: STAT 519 and one of STAT 512, 513, 514, 516, 517; or instructor permission.
Includes order statistics, distribution-free statistics, U-statistics, rank tests and estimates, asymtotic efficiency, Bahadur efficiency, M-estimates, one- and two-way layouts, multivariate location models, rank correlation, and linear models.

STAT 718 - (3) (O)
Sample Surveys
Prerequisite: MATH 312 or 510, or instructor permission.
An introduction to the design and analysis of sample surveys. Topics include simple random sampling, stratified sampling, multistage (cluster) sampling, double sampling, ratio and regression estimates. Theoretical discussions are supplemented by computer simulated surveys, and studies of the documentation of ongoing government sample surveys.

STAT 719 - (3) (SI)
Statistical Computing
Prerequisite: STAT 512 and 518, or instructor permission.
Studies computational methods for multiple linear regression, unconstrained optimization and non-linear regression, model-fitting based on L_p norms, and robust estimation.

STAT 720 - (3) (Y)
Advanced Probability Theory for Applied Scientists
Prerequisite: MATH 531 or instructor permission.
The course will emphasize those techniques which are important for the applied statistician: various forms of convergence for random variables, central limit theorems, asymptotics for a transformation of a sequence of random variables, and an introduction to martingales.

STAT 721 - (3) (O)
Advanced Linear Models
Prerequisite: MATH 351, STAT 512, 513, 519, or instructor permission.
Review of matrix theory (various types of generalized inverses and their properties). Theory and analysis of fixed effects linear models. Estimation of variance components in random and mixed effects linear models. Various methods of estimation of variance components such as: Henderson’s three methods, MLE, RMLE, MINQUE (and its modifications). Theory and analysis of random and mixed effects models.

STAT 731 - (3) (O)
Advanced Data Analysis
Prerequisite: STAT 512 and 513, or instructor permission.
Includes modern computer-intensive methods of data analysis, including splines and other methods of nonparametric regression, bootstrap, techniques for handling missing values and data reduction, nonlinear regression, graphical techniques, and penalized maximum likelihood estimation.

STAT 812 - (3) (SI)
Topics in Statistics
Study of topics in statistics that are currently the subject of active research.

STAT 817 - (3) (SI)
Advanced Time Series
Prerequisite: MATH 736, STAT 517, or instructor permission.
Introduces stationary stochastic processes, related limit theorems, and spectral representations. Includes an asymtotic theory for estimation in both the time and frequency domains.

STAT 831 - (3) (O)
Advanced Survival Analysis
Prerequisite: STAT 514, 519, 720 (or MATH 736), and 731, or instructor permission. MATH 511 is recommended, but not required.
Includes the Martingale theory and the counting process approach to survival analysis, asymtotic theory of the Cox and related models, censoring, competing risks, multiple events per subject, parametric survival models, advanced model diagnostics for the Cox model, time-dependent covariates, bootstrap model validation, and frailty models.

STAT 832 - (3) (SI)
Topics in Biostatistics
Study of topics in biostatistics that are currently the subject of active research.

STAT 912 - (3) (Y)
Statistics Seminar
Advanced graduate seminar in current research topics. Offerings in each semester are determined by student and faculty research interests.

STAT 995 - (1-3) (Y)
Statistical Consulting
Prerequisite: Current registration in the statistics graduate program, or instructor permission.
Introduces the practice of statistical consultation. A combination of formal lectures, meetings with clients of the statistical consulting service, and sessions in the statistical computing laboratory.

STAT 996 - (3-9) (Y)
Directed Reading
Research into current statistical problems under faculty supervision.

STAT 997 - (3-12) (Y)
Non-Topical Research, Preparation for Doctoral Research
For doctoral research, taken before a dissertation director has been selected.

STAT 999 - (3-12) (Y)
Non-Topical Research
For doctoral research, taken under the supervision of a dissertation director.

The Statistics Colloquium The colloquium is held weekly, with the sessions devoted to research activities of students and faculty members, and to lectures by visiting statisticians on current research interests.