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STATISTICAL SCIENCE
Professor Wayne A. Woodward, Department Chair
Professors: Ronald Butler, Richard Gunst, William R. Schucany, S. Lynne Stokes, Wayne A. Woodward; Associate Professors:Ian Harris, Monnie McGee; Assistant Professors: Tony Ng, Sherry Wang, Jing Cao; Emeritus Professors: U. Narayan Bhat, Henry L. Gray, C.H. Kapadia, Campbell B. Read.
The Department of Statistical Science offers M.S. and Ph. D. degrees in statistical science. These programs integrate both theory and practice by providing a strong theoretical foundation through courses in mathematical statistics, probability and stochastic processes and by covering the intricacies of the practice of statistics through courses with an applied orientation, as well as hands-on experience in statistical consulting.
Admission Requirements
Minimum requirements for admission to the graduate program in statistical science are: Applicants must hold a bachelor’s degree in mathematics, statistics, engineering, a natural or social science or business administration with mathematics through advanced calculus and linear algebra.
Degree of Master of Science
Degree Requirements
To qualify for the M.S. degree, the student must successfully complete at least 36 hours of coursework acceptable to the departmental faculty, including STAT 6304, 6327, 6328, 6336 and 6337; must pass a written examination (called the basic examination) on the required coursework; and must prepare an acceptable report and oral examination on analysis and interpretation of a data set provided by an examination committee.
Degree of Doctor of Philosophy
Advancement to Candidacy
To qualify for the Ph.D. degree in statistics, the student must (1) satisfy
all curricular requirements as specified by the departmental faculty (at least
36 hours), including the courses listed for the Master of Science as well as
STAT 6371 and 7327; (2) pass the basic exam, typically at the end of the first
year; (3) pass a written exam (called the comprehensive exam) to assess the
student’s readiness for research, typically at the end of the second
year; (4) complete a minimum of three years of graduate academic work, at least
one of which is in full-time residence on the campus of Southern Methodist
University or at a research facility approved by the departmental faculty and
the dean of research and graduate studies; and (5) write and make a successful
defense of the dissertation. See the Degree Requirements section of this catalog
for general requirements for the Ph.D. degree.
A student will advance to candidacy after he or she passes the basic and comprehensive
exams, prepares a written prospectus in a research area on which the dissertation
will be based and presents it orally and receives approval of the prospectus
from his or her dissertation committee.
The Courses (STAT)
Note: 5000-level courses in statistical science do not carry graduate credit for students in the M.S. program or in the Ph.D. program in statistical science.
5340 (CSE 5370). Probability and Statistics for Scientists and Engineers. Introduction to fundamentals of probability and distribution theory and statistical techniques used by engineers and physical scientists. Examples of tests of significance, operating characteristic curve, tests of hypothesis about one and two parameters, estimation, analysis of variance and the choice of a particular experimental procedure and sample size. Prerequisites: MATH 1337, 1338 and 2339 or equivalent.
5344. Statistical Quality Control. Statistics and simple probability are introduced in terms of problems that arise in manufacturing and their application to control of manufacturing processes. Acceptance sampling in terms of standard sampling plans, including MilStd 105, MilStd 414, Dodge-Romig plans and continuous sampling plans. Prerequisite: Any one of STAT 4340, 5340, CSE 4340 or 5370.
5371. Experimental Statistics I. A non-calculus development of the fundamental procedures of applied experimental statistics, including tests of hypotheses and interval estimation for the normal, binomial, chi-square and other distributions and nonparametric tests. Prerequisite: Junior standing or permission of the instructor.
5372. Experimental Statistics II. Analysis of variance, completely randomized design, randomized complete block design, nested classifications and factorials. Analysis of covariance, simple and multiple linear regression and correlation. Prerequisite: STAT 5371.
5377 (CSE 5377). Statistical Design and Analysis of Experiments. Introduction to statistical principles in the design and analysis of industrial experiments. Completely randomized, randomized complete, incomplete block, Latin square and Plackett-Burman screening designs. Complete and fractional factorial experiments. Descriptive and inferential statistics. Analysis of variance models. Mean comparisons. Prerequisite: Senior standing with a science or engineering major or permission of the instructor.
5385. Introductory Nonparametric Statistics. Introduction to nonparametric statistics with examples in the behavioral sciences, including choice and use of rank tests, runs test and rank order correlation. Tests for one-sample and two-sample cases. Prerequisite: STAT 5371, 5340/CSE 5370 or equivalent.
6304. Computational Statistics. Introduction to the fundamentals of statistical computing widely used by both theoretical and applied statisticians in both academics and industry. Subject matter is divided into two areas: simulation experiments and statistical software. Includes generating random deviates from various distributions, analysis of statistical algorithms, an introduction to UNIX, an introduction to S-Plus for data analysis and graphics, interfacing S-Plus to code written in C and/or FORTRAN and managing and manipulating very large data sets. Prerequisite: STAT 6327 or concurrent enrollment in this course.
6327. Mathematical Statistics. Theory of probability distributions. Random variables and functions of random variables. Multivariate and conditional distributions. Sampling distributions and order statistics. Expected value, transformations and approximations. Prerequisite: advanced calculus or permission of the instructor.
6328. Mathematical Statistics. Sufficiency and completeness. Unbiased, maximum likelihood and Bayes point estimators and minimizing risk. Confidence sets. Most powerful, uniformly MP and likelihood ratio tests. Large-sample approximations and contingency table analysis. Prerequisite: STAT 6327.
6336. Statistical Analysis. Analysis of data from one and two samples assuming normal distributions and independent errors. Discussion of paired sample analyses, Goodness of Fit and categorical data analysis topics. Introduction to simple linear regression analysis.
6337. Statistical Analysis. Emphasis on application of statistical principles in the design of experiments. Complete and fractional factorials, blocking, nesting, replication and randomization. Analysis of data from classical multifactor experimental designs with fixed and random effects. Multiple comparisons and contrasts of main effects and interactions. Prerequisite: STAT 6336.
6342. Advanced Statistical Quality Control. Investigation of statistical methods and management principles useful for understanding and improving measurable performance in human endeavors. Development of a “statistical thinking” foundation through the evaluation of case studies and class labs. Prerequisite: STAT 4340/CSE 4340 or STAT 5340/CSE 5370 or STAT 5371. Or, corequisite: STAT 6327 or 6336.
6345. Linear Regression. The classical tools of linear regression based upon least squares estimation and inference through the assumption of normally distributed errors. Topics in model formulation, data transformations, variable selection and regression diagnostics for influential observations. Collinear predictors and biased estimation. Survey of alternatives to least squares. Prerequisite: STAT 6337.
6346. Advanced Regression Analysis. Nonlinear least-squares estimation. Theory and applications of generalized linear models. Estimation, asymptotic distribution theory and tests for model parameters. Topics in spatial statistical modeling, including variogram estimation and kriging. Prerequisite: STAT 6345 or permission of the instructor.
6350. Analysis of Lifetime Data. Statistically based methods for analysis of life testing and failure data from complete and censored samples. Topics include statistical lifetime distributions; types of censoring, probability and other graphical techniques; nonparametric and parametric estimation methods; and lifetime data regression. Prerequisites: STAT 6304, 6327, 6328, 6336, 6337 or equivalent.
6355. Applied Multivariate Analysis. Statistical methods of analysis of multivariate data, tests and estimation of multivariate normal parameters. Hotelling’s T2, discriminant analysis, canonical correlation, principal components and factor analysis. Applications are emphasized. Prerequisite: STAT 6337.
6358. Topics in Biostatistics. Introduction to various statistical methods that are widely used in the biosciences, especially biomedical research. Includes survival analysis, contingency tables, logistic regression, analysis of longitudinal data, design of clinical experiments, epidemiology and statistical genetics. Topics may vary with instructor. Prerequisite: STAT 6328 or permission of the instructor.
6363. Time Series Analysis. Statistical methods of analyzing time series. Autocorrelation function and spectrum. Autoregressive and moving average processes. More general models, forecasting and stochastic model building. Prerequisite: Permission of the instructor.
6366. Statistical Consulting. Apprenticeship under an experienced consultant, with exposure to real problems handled by the Center for Statistical Consulting and Research. Between four to six hours per week will be spent in consultation sessions and seminars. In addition to a variety of technical statistical issues, the class will study the existing literature on the nonstatistical aspects of the consulting endeavor.
6370 (CSE 6370). Stochastic Models. Model building with stochastic processes in applied sciences. Phenomena with uncertain outcomes are formulated as stochastic models and their properties are analyzed. Some specific problems discussed come from areas such as population growth, queuing, reliability, time series and social and behavioral processes. Statistical properties of the models are emphasized. Prerequisites: STAT 5340/CSE 5370 and graduate standing.
6371. Probability Theory. An introduction to measurement of theoretic probability. Random variables, expectation, conditional expectation and characteristic functions. Prerequisite: STAT 6327 or permission of the instructor.
6372 (CSE 6372). Queueing Theory. Queueing theory provides the theoretical basis for the analysis of stochastic service systems. The underlying stochastic processes are point processes of which Markov and renewal processes are two major examples. The emphasis of the course is in the formulation of queueing models and their behavioral and statistical analyses using Markov and renewal techniques. Prerequisite: An introductory course in Stochastic Processes (such as STAT 6370/CSE 6370, STAT 6376, 6379 or EE 5306).
6375. Sequential Analysis. Statistical inference when sample size is not predetermined. Stopping rules, sequential probability ratio tests, composite hypotheses, Bayes rules and sequential estimation. Prerequisite: STAT 6328.
6376. Stochastic Processes. Random walk, Markov processes, Poisson processes, waiting times, spectral density functions and applications to random noise problems. Prerequisite: STAT 6327.
6377. Multivariate Categorical Data Analysis. Structural models for counting data. The general log-linear model for contingency tables is introduced along with likelihood-ratio tests, hierarchical models and partitioning of likelihood-ratio statistics. Prerequisites: STAT 6328, 6337 or permission of the instructor.
6378. Multivariate Analysis. Theory and inference in the multivariate normal distribution. Regression, correlation, Wishart distribution, Hotelling’s T2, MANOVA and discriminant analysis. Prerequisite: STAT 6320 and 6328 or 6381.
6379. Introduction to Markov Processes. Branching processes, recurrent events, random walk, finite Markov chains and simplest time-dependent stochastic processes. Prerequisite: STAT 6327 or 6370/CSE 6370.
6380. Mathematical Theory of Sampling. Theorems concerning simple random sampling, stratified random sampling, cluster sampling, unequal probability sampling, ratio estimates, regression estimates, etc. Prerequisite: STAT 6328.
6381. Theory of Linear Models I. Theory of the general linear model. Estimatibility and testability. Theory of analysis of fixed, random and mixed models. Prerequisites: STAT 6328, 6337.
6382. Theory of Linear Models II. Variance component models, mixed models, intra-block analysis, incomplete block designs and factorials and fractional replicates. Prerequisite: STAT 6381.
6385. Survey of Nonparametric Statistics. Robust and distribution-free techniques, order statistics, EDF statistics, quantiles, asymptotic distributions and tolerance intervals. Linear rank statistics for one, two and several sample problems involving location and scale. Runs, multiple comparison, rank correlation and asymptotic relative efficiency. Prerequisite: STAT 6328.
6386. Nonparametric Statistics. Continuation of topics covered in STAT 6385, including linear rank statistics and asymptotic relative efficiency. Also includes U-statistics, robustness, M-estimation, minimum distance estimation, adaptive procedures, density estimation, aligned ranks, jackknifing and bootstrapping. Prerequisite: STAT 6385.
6388. Large Sample Theory. Limit theorems useful in mathematical statistics. The foundation of asymptotic theory in statistics including modes of convergence, laws of large numbers and the central limit theorem. Systematic coverage of useful representations of certain basic statistics and large sample optimality of maximum likelihood procedures. Prerequisites: STAT 6328, 6371.
6390. Bayesian Statistics. An introduction to Bayesian inference. Covers current approaches to Bayesian modeling and computation. Prerequisite: STAT 6328.
6395. Special Topics in Statistics.
6398, 6399. Thesis.
7011. Supervised Internship. Supervised experience in statistical consulting, carried out as an internship in approved work settings outside the Center for Statistical Consulting and Research. Prerequisite: STAT 6304, 6327, 6328, 6336, 6337 or equivalent.
7100, 7300. Seminar.
7110, 7111, 7112. Seminar in Statistical Literature. Reports from papers in statistical journals, bibliographical problems, etc.
7327. Advanced Statistical Inference. Topics in statistical inference, estimation (point and interval estimates, Bayesian and likelihood), tests of hypotheses (invariant, unbiased, most powerful, conditional and Bayesian) and large-sample theory for multiparameter problems. Prerequisite: STAT 6371.
7362. Advanced Special Topics.
7363. Theory and Application of Spectral Analysis. Intended for advanced graduate students who want to do research in spectral analysis or who have a major interest in time series. Prerequisites: One term of stochastic processes (STAT 6376) and one term of time series (STAT 6363) or permission of the instructor.
8313. Research in Statistical Inference.
8196, 8396. Dissertation.
8197, 8397, 8697. Dissertation.
8198, 8398, 8698. Dissertation.
8199, 8399, 8699. Dissertation.
