Statistics (STAT)

STAT 5305. Advanced Probability and Statistics.

This course covers advanced mathematical and probabilistic theories underlying statistical inference. Topics include data description, probability distributions, sampling and sampling distributions, confidence intervals, and hypothesis testing for both categorical and quantitative data. Emphasis is placed on the theoretical foundations of statistical methods, as well as their proper application and interpretation. Students examine assumptions, variability, randomness, and inferential reasoning within a rigorous mathematical framework. Through analytical and computational approaches, the course develops a deeper understanding of statistical inference and prepares students for advanced study or applied work in statistics and related fields.

STAT 5315. Mathematical Statistics.

This course examines the theoretical foundations of statistical inference at the graduate level. Topics include convergence of random variables, parameter estimation, properties of estimators, interval estimation, sufficiency and applications to the exponential family, hypothesis testing, decision theory, and Bayesian inference. Emphasis is placed on rigorous mathematical formulation and analysis of inferential procedures, as well as understanding their assumptions and limitations. Selected applications are used to illustrate theoretical concepts without shifting focus from underlying statistical theory. The course prepares students for advanced study and research in statistics.

STAT 5325. Design and Analysis of Experiments.

This course introduces graduate‑level principles and methods in the design and analysis of experiments. Topics include randomization, blocking, justification of linear models, and fundamental principles underlying experimental design. The course examines the construction and analysis of common experimental designs such as completely randomized designs, randomized block designs, factorial and fractional factorial designs, composite designs, and incomplete block designs. Emphasis is placed on understanding the statistical models that support experimental analysis, interpretation of results, and assessment of design efficiency.

STAT 5335. Survival Analysis.

This course introduces graduate‑level concepts and methods for the analysis of survival, or time‑to‑event, data. Topics include characteristics of survival data, survival and hazard functions, parametric models for survival time, and maximum likelihood estimation of survival functions. The course also covers nonparametric and semi‑parametric methods, two‑sample testing procedures, regression models for survival data, and graphical and mathematical techniques for model assessment. Emphasis is placed on understanding assumptions, handling censoring and truncation, and interpreting results within a rigorous statistical framework. Prerequisite: Math 5305 or STAT 5305 with a grade of "B" or better.

STAT 5345. Regression Analysis.

This course introduces graduate‑level theory and methodology for regression analysis. Topics include formulation of simple and multiple regression models, assessment of model assumptions and fit, model design, and criteria for selecting appropriate regression models. Emphasis is placed on statistical inference, diagnostic techniques, and interpretation of regression results. Students also develop experience using statistical software to analyze data and communicate findings through written reports based on real‑world datasets. The course integrates theoretical understanding with applied analysis to prepare students for advanced study or professional work involving regression modeling.

STAT 5347. Introduction to Data Science.

This course introduces graduate‑level concepts and methods in data science. Topics include data wrangling, data exploration and visualization, and supervised learning methods for regression and classification problems. In addition, tree-based models, neural networks and unsupervised learning methods such as principal component analysis and cluster analysis will also be covered. The material will be approached with a blend of theory and application, and will include programming in R, Python, or another modern, popular language of the instructor’s choice.

STAT 5376B. Analysis of Variance.

This course introduces graduate‑level methods for analysis of variance (ANOVA). Topics include one‑way, two‑way, and multifactor ANOVA models, along with underlying assumptions, estimation, and hypothesis testing procedures. The course emphasizes the formulation and interpretation of ANOVA models, including the use of linear contrasts and random effects. Students examine how experimental design influences variance structure and inference. Statistical software is used to implement ANOVA methods and interpret results in applied contexts. The course prepares students to analyze experimental and observational data using appropriate variance‑based techniques.

STAT 5376D. Statistical Applications in Genetics and Bioinformatics.

This course examines applications of statistical methods in genetics and bioinformatics at the graduate level. Students study statistical techniques used to analyze large‑scale genetic and bioinformatic data, including high‑throughput genomic and epigenetic datasets such as microarray and sequencing data. Topics may include analysis of variance, regression analysis, hidden Markov models, and other statistical tools commonly used in biological data analysis. Emphasis is placed on model formulation, methodological assumptions, interpretation of results, and challenges arising from complex and high‑dimensional data. The course integrates statistical theory with applied analysis to prepare students for research and advanced study in statistical genetics and bioinformatics.

STAT 5390. Statistics.

This course introduces fundamental statistical concepts and methods along with their mathematical and probabilistic foundations. Emphasis is placed on statistical reasoning, simulation, and modeling as tools for understanding variability and uncertainty. Topics include data collection and experimental design, probability models, sampling distributions, estimation, hypothesis testing, and regression analysis. Students examine the planning, analysis, interpretation, and reporting of experimental and observational data using appropriate statistical methods. The course integrates theory with applied analysis to prepare students for advanced coursework, teaching, or applied statistical work requiring a solid foundation in statistical methodology.

STAT 7325. Statistics I.

This course examines the mathematical and probabilistic foundations of statistical inference at the doctoral level. Topics include sampling methods, sampling distributions, confidence intervals, and hypothesis testing. Emphasis is placed on understanding inferential procedures through both analytical derivations and simulation‑based approaches. Students study the assumptions underlying statistical methods and the interpretation of inferential results within a rigorous mathematical framework. The course prepares students for advanced theoretical or applied coursework in statistics and for the use of statistical inference in research contexts.

STAT 7335. Statistics II: Linear Modeling.

This course examines the formulation, theory, and application of linear statistical models at the doctoral level. Topics include least‑squares estimation, the general linear hypothesis, the Gauss–Markov theorem, assessment of model fit, effects of departures from model assumptions, model design, and criteria for selection of optimal regression models. Emphasis is placed on statistical inference for model parameters and on understanding the theoretical properties of estimators. Analytical derivations are integrated with applied analysis to support research applications. Prerequisite: MATH 7325 or STAT 7325 with a grade of "B" or better.

STAT 7337. Advanced Mathematical Statistics.

This course examines advanced theory in classical and modern mathematical statistics at the doctoral level. Topics include multivariate normal distributions, the central limit theorem and related conditions, principles of data reduction, the delta method, and asymptotic theory for likelihood‑based inference. The course also covers decision‑theoretic approaches to estimation and hypothesis testing, including concepts such as minimaxity and admissibility, and bootstrap. Emphasis is placed on rigorous derivations, theoretical properties of statistical procedures, and preparation for advanced research in statistics.

STAT 7345. Advanced Linear Modeling.

This course extends linear regression methodology to more general modeling frameworks in which standard assumptions are relaxed or violated. Topics include generalized least squares, generalized linear models, and mixed effects models, with emphasis on estimation, inference, and model interpretation. The course addresses correlated and non-normal data structures commonly encountered in applied research, preparing students to analyze complex data arising in scientific, social science, and professional contexts. Prerequisite: STAT 7335 with a grade of "B" of better.

STAT 7355. Time Series Analysis.

This course covers the analysis of time-dependent data with an emphasis on statistical modeling, inference, and forecasting for time series. Topics include stationary time series, estimation and interpretation of autocorrelation and partial autocorrelation functions, modeling and forecasting using autoregressive moving average (ARMA) models, spectral analysis, and methods for analyzing nonstationary and seasonal time series. Applications highlight the use of time series techniques in scientific and data-driven contexts where temporal dependence plays a central role in data analysis and decision making. Prerequisite: STAT 5305 or STAT 7325 with a grade of "B" of better.

STAT 7375E. Computational Statistics.

This course examines computational methods and algorithms used in modern statistical analysis. Topics include sampling and optimization techniques such as acceptance–rejection methods, importance sampling, Markov chain Monte Carlo algorithms, Fisher scoring, expectation–maximization algorithms, and minorization–maximization methods. Emphasis is placed on understanding the theoretical foundations of these algorithms and their role in statistical inference and estimation. Students study how computational approaches are used to generate random samples, approximate complex quantities, and estimate parameters in statistical models.

STAT 7375F. Multivariate Data Analysis.

This course examines statistical theory and methodology for the analysis of multivariate data at the doctoral level. Topics include the multivariate normal distribution, hypothesis testing for mean vectors, multivariate analysis of variance, discriminant analysis, and methods for dimension reduction such as principal component analysis, factor analysis, and canonical correlation analysis. Emphasis is placed on theoretical foundations, statistical inference, and interpretation of multivariate techniques. The course prepares students for advanced study and research involving multivariate statistical methods and their application in a variety of research contexts.

STAT 7375G. Bayesian Methods.

This course examines Bayesian statistical methods and their theoretical foundations at the graduate level. Topics include Bayesian inference for one‑parameter and multi‑parameter models, prior specification, posterior computation, and formulation of regression models within the Bayesian framework. Emphasis is placed on understanding Bayesian reasoning, model formulation, and interpretation of posterior results. Computational tools are used to support Bayesian data analysis and to illustrate theoretical concepts. The course prepares students for advanced research and applications involving Bayesian statistical methods.

STAT 7375I. Advanced Statistical Learning.

This course examines advanced theoretical foundations of statistical learning and deep learning at the doctoral level. Topics include empirical risk minimization, metric entropy, Vapnik-Chervonenkis dimension, Rademacher and Gaussian complexity, symmetrization and chaining techniques, contraction principles, uniform laws of large numbers, and sample complexity. The course also introduces theoretical perspectives on neural networks within the statistical learning framework. Emphasis is placed on rigorous mathematical analysis, generalization theory, and asymptotic behavior of learning algorithms. Prerequisite: MATH 7337 or STAT 7337 with a grade of "B" or better.

STAT 7387. Consulting.

This course focuses on developing skills in the collaborative practice of mathematics and statistics. This will be done through class discussion, readings, and different projects. Students will learn how to apply mathematics or statistics to solve real-world problems through case studies and collaborative projects. They will also learn how to apply ethical considerations to their professional practice. Taking this course will allow students to gain skills in problem solving and providing mathematical and statistical consulting services. Prerequisite: STAT 7325 with a grade of "B" or better.