PhD Programs

Note: 5000-level courses in Statistical Science do not carry graduate credit for students in the Ph.D. program in Statistical Science.

**6304: Computational Statistics.** Designed to introduce students to the fundamentals of statistical computing. Introduces computational methods in statistics with emphasis on the use of statistical software packages, statistical simulation, numerical methods, and related topics. Topics include introduction to R and other statistical software for statistical analysis and graphics; generating random deviates from various distributions; and the use of Monte Carlo methods for solving optimization problems. Prerequisite: STAT 5373 or STAT 6327 or concurrent enrollment in these courses.

**6320: Quadratic Forms and Matrix Computations.** Statistical distribution theory of quadratic forms of normal variables. Matrix and vector operations as they pertain to the distribution of quadratic forms. Distributions, moments, and independence of quadratic forms. Computer implementation using SAS. Prerequisite: Linear Algebra.

**6327: Mathematical Statistics.** Theory of probability distributions. Random variables and functions of random variables. Multivariate and conditional distributions. Sampling distributions; order statistics. Expected value, transformations, approximations. Prerequisite: Advanced Calculus or permission of instructor.

**6328: Mathematical Statistics.** Sufficiency and completeness. Unbiased, maximum likelihood and Bayes point estimators, minimizing risk. Confidence sets. Most powerful, uniformly MP and likelihood ratio tests. Large-sample approximations; 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, 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.** Investigate statistical methods and management principles useful for understanding and improving measurable performance in human endeavors. Develop 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 instructor.

**6350: Analysis of Lifetime Data. **Statistically based methods for analysis of life testing and failure data from complete and censored samples. Includes topics such as statistical lifetime distributions; types of censoring; probability and other graphical techniques; nonparametric and parametric estimation methods; and lifetime data regression. Prerequisites: STAT 6304, 6328, 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. Prerequisites: STAT 6337 .

**6358: Topics in Biostatistics.** Introduction to various statistical methods that are widely used in the biosciences, especially biomedical research. Subject matter 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 instructor.

**STAT 6360: Statistical Methods in Epidemiology. **This course presents an introduction to epidemiologic principles and statistical methods used in biomedical research. Topics involve the design, analysis, and interpretation of biomedical study results. Prerequisites: 5372, 5374, and 5304 or permission of instructor.

**6363: Time Series Analysis.** Statistical methods of analyzing time series. Autocorrelation function and spectrum. Autoregressive and moving average processes. More general models, forecasting, stochastic model building. Prerequisite: Permission of 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 measure theoretic probability. Random variables, expectation, conditional expectation, characteristic functions. Prerequisite: STAT 6327 or permission of 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 (e.g. STAT 6370/CSE 6370, STAT 6376, 6379, EE 5306).

**6375: Sequential Analysis.** Statistical inference when sample size is not predetermined. Stopping rules, sequential probability ratio tests, composite hypotheses, Bayes rules, sequential estimation. Prerequisite: STAT 6328.

**6376: Stochastic Processes.** Random walk, Markov processes, Poisson processes, waiting times, spectral density functions, 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 and 6337, or permission of 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, 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 and 6337.

**6382: Theory of Linear Models II.** Variance component models, mixed models, intra-block analysis, incomplete block designs and factorials, fractional replicates. Prerequisite: STAT 6381.

**6385: Survey of Nonparametric Statistics.** Topics include 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. Additional topics include 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 and 6371.

**6390: Bayesian Statistics.** An introduction to Bayesian inference. Covers current approaches to Bayesian modeling and computation. Prerequisite: STAT 6328.

**STAT 6391: Bayesian Hierarchical Modeling. ** The course focuses on how to account for spatial, temporal, and other complex correlation structures and incorporate prior information into a statistical analysis using modern computer software packages (i.e., WinBUGS and R). Prerequisite: STAT 6390: Bayesian Statistics

**6395: Special Topics in Statistics.**

**7327: Advanced Statistical Inference.** Topics in statistical inference; estimation (point and interval estimates, Bayesian and likelihood); tests of hypotheses (invariant, unbiased, most powerful, conditional, Bayesian); large-sample theory for multiparameter problems. Prerequisite: STAT 6328.

**7362: Advanced Special Topics.**

**7363: Time Series Analysis II** Intended for advanced graduate students who intend to do research in time series analysis or who have a major interest in time series. Prerequisites: One term of time series (STAT 6363), or permission of instructor.