Department of Statistics and Operations Research (GRAD)

Linear, integer, nonlinear, and dynamic programming, classical optimization problems, network theory.

Introduction to mathematical theory of probability covering random variables; moments; binomial, Poisson, normal and related distributions; generating functions; sums and sequences of random variables; and statistical applications. Students may not receive credit for both STOR 435 and STOR 535.

Introduction to Markov chains, Poisson process, continuous-time Markov chains, renewal theory. Applications to queueing systems, inventory, and reliability, with emphasis on systems modeling, design, and control.

Review of basic inference; two-sample comparisons; correlation; introduction to matrices; simple and multiple regression (including significance tests, diagnostics, variable selection); analysis of variance; use of statistical software.

Probability models for long-term insurance and pension systems that involve future contingent payments and failure-time random variables. Introduction to survival distributions and measures of interest and annuities-certain.

Short term probability models for potential losses and their applications to both traditional insurance systems and conventional business decisions. Introduction to stochastic process models of solvency requirements.

This course will introduce students to the healthcare industry and provide hands-on experience with key actuarial and analytical concepts that apply across the actuarial field. Using real world situations, the course will focus on how mathematics and the principles of risk management are used to help insurance companies and employers make better decisions regarding employee benefit insurance products and programs.

Examines selected topics from statistics and operations research. Course description is available from the department office.

Requires permission of the department. Statistics and analytics majors only. An opportunity to obtain credit for an internship related to statistics, operations research, or actuarial science. Pass/Fail only. Does not count toward the statistics and analytics major or minor.

Permission of the director of undergraduate studies. This course is intended mainly for students working on honors projects. May be repeated for credit.

This is an upper-level course focusing on optimization aspects of common and practical problems and topics in statistical learning, machine learning, neural networks, and modern AI. It covers several topics such as optimization perspective of linear regression, nonlinear regression, matrix factorization, stochastic gradient descent, regularization techniques, neural networks, deep learning techniques, and minimax models.

An introduction to algorithms and modeling techniques that use knowledge gained from prior experience to make intelligent decisions in real time. Topics include Markov decision processes, dynamic programming, multiplicative weights update, exploration vs. exploitation, multi-armed bandits, and two player games.

This course provides hands-on experience working with data sets provided in class and downloaded from certain public websites. Lectures cover basic topics such as R programming, visualization, data wrangling and cleaning, exploratory data analysis, web scraping, data merging, predictive modeling, and elements of machine learning. Programming analyses in more advanced areas of data science. Students may not receive credit for both STOR 320 and STOR 520.

This course is an advanced undergraduate course in probability with the aim to give students the technical and computational tools for advanced courses in data analysis and machine learning. It covers random variables, moments, binomial, Poisson, normal and related distributions, generating functions, sums and sequences of random variables, statistical applications, Markov chains, multivariate normal and prediction analytics. Students may not receive credit for both STOR 435 and STOR 535.

This course will survey the history of sports analytics across multiple areas and challenge students in team-based projects to practice sports analytics. Students will learn how applied statistics and mathematics help decision makers gain competitive advantages for on-field performance and off-field business decisions.

Functions of random samples and their probability distributions, introductory theory of point and interval estimation and hypothesis testing, elementary decision theory.

This course covers the fundamental theory and methods for time series data, as well as related statistical software and real-world data applications. Topics include the autocorrelation function, estimation and elimination of trend and seasonality, estimation and forecasting procedures in ARMA models and nonstationary time series models.

The course covers advanced data analysis methods beyond those in STOR 455 and how to apply them in a modern computer package, specifically R or R-Studio which are the primary statistical packages for this kind of analysis. Specific topics include (a) Generalized Linear Models; (b) Random Effects; (c) Bayesian Statistics; (d) Nonparametric Methods (kernels, splines and related techniques).

Introduction to theory and methods of machine learning including classification; Bayes risk/rule, linear discriminant analysis, logistic regression, nearest neighbors, and support vector machines; clustering algorithms; overfitting, estimation error, cross validation.

Deep neural networks (DNNs) have been widely used for tackling numerous machine learning problems that were once believed to be challenging. With their remarkable ability of fitting training data, DNNs have achieved revolutionary successes in many fields such as computer vision, natural language progressing, and robotics. This is an introduction course to deep learning.

This upper-level-undergraduate and beginning-graduate-level course introduces the concepts of modeling, programming, and statistical analysis as they arise in stochastic computer simulations. Topics include modeling static and discrete-event simulations of stochastic systems, random number generation, random variate generation, simulation programming, and statistical analysis of simulation input and output.

Examines selected topics from statistics and operations research. Course description is available from the department office.

STOR 612 consists of three major parts: linear programming, quadratic programming, and unconstrained optimization. Topics: Modeling, theory and algorithms for linear programming; modeling, theory and algorithms for quadratic programming; convex sets and functions; first-order and second-order methods such as stochastic gradient methods, accelerated gradient methods and quasi-Newton methods for unconstrained optimization.

STOR 614 consists of three major parts: Integer programming, conic programming, and nonlinear optimization. Topics: modeling, theory and algorithms for integer programming; second-order cone and semidefinite programming; theory and algorithms for constrained optimization; dynamic programming; networks.

Required preparation, advanced calculus. Lebesgue and abstract measure and integration, convergence theorems, differentiation. Radon-Nikodym theorem, product measures. Fubini theorems. Lp spaces.

Foundations of probability. Basic classical theorems. Modes of probabilistic convergence. Central limit problem. Generating functions, characteristic functions. Conditional probability and expectation.

The aim of this 3-credit graduate course is to introduce stochastic modeling that is commonly used in various fields such as operations research, data science, engineering, business, and life sciences. Although it is the first course in a sequence of three courses, it can also serve as a standalone introductory course in stochastic modeling and analysis. The course covers the following topics: discrete-time Markov chains, Poisson processes, and continuous-time Markov chains.

This 3-credit course is the second graduate-level course on stochastic modeling that expands upon the material taught in STOR 641. The course covers the following topics: renewal and regenerative processes, queueing models, and Markov decision processes.

Required preparation, two semesters of advanced calculus. Probability spaces. Random variables, distributions, expectation. Conditioning. Generating functions. Limit theorems: LLN, CLT, Slutsky, delta-method, big-O in probability. Inequalities. Distribution theory: normal, chi-squared, beta, gamma, Cauchy, other multivariate distributions. Distribution theory for linear models.

Point estimation. Hypothesis testing and confidence sets. Contingency tables, nonparametric goodness-of-fit. Linear model optimality theory: BLUE, MVU, MLE. Multivariate tests. Introduction to decision theory and Bayesian inference.

Permission of the instructor. Basics of linear models: matrix formulation, least squares, tests. Computing environments: SAS, MATLAB, S+. Visualization: histograms, scatterplots, smoothing, QQ plots. Transformations: log, Box-Cox, etc. Diagnostics and model selection.

ANOVA (including nested and crossed models, multiple comparisons). GLM basics: exponential families, link functions, likelihood, quasi-likelihood, conditional likelihood. Numerical analysis: numerical linear algebra, optimization; GLM diagnostics. Simulation: transformation, rejection, Gibbs sampler.

Introduces students to modeling, programming, and statistical analysis applicable to computer simulations. Emphasizes statistical analysis of simulation output for decision-making. Focuses on discrete-event simulations and discusses other simulation methodologies such as Monte Carlo and agent-based simulations. Students model, program, and run simulations using specialized software. Familiarity with computer programming recommended.

The purpose of this course is to provide a strong foundation in computational skills needed for reproducible research in data science and statistics. Topics will include computational tools and programming skills to facilitate reproducibility, as well as procedures and methods for reproducible conclusions.

Examines selected topics from statistics and operations research. Course description is available from the department office.

Permission of the department. Majors only. Individual reading, study, or project supervised by a faculty member.

Permission of the department. Majors only. Individual reading, study, or project supervised by a faculty member.

This course is designed to give Statistics & Analytics (STAN) majors an opportunity to integrate and apply the knowledge and skills acquired throughout the STAN degree. At the beginning of the semester, the instructor will present to the class a broad description of several problems originating from external industry partners, and covering a wide range of statistics, modeling, optimization, and data science topics. Students will work on these problems throughout the remainder of the semester.

This seminar course is intended to give Ph.D. students exposure to cutting edge research topics in statistics and operations research and assist them in their choice of a dissertation topic. The course also provides a forum for students to meet and learn from major researchers in the field.

This seminar course is intended to give Ph.D. students exposure to various issues and pedagogy in teaching statistics and operations research. The course also provides a forum for students to observe and learn from current teaching faculty. Students should register for one credit only. STOR Ph.D. students only.

This course will provide a detailed and deep treatment for commonly used methods in continuous optimization, with applications in machine learning, statistics, data science, operations research, among others.

Advanced theory for nonlinear optimization. Algorithms for unconstrained and constrained problems.

Techniques for formulating and solving discrete valued and combinatorial optimization problems. Topics include enumerative and cutting plane methods, Lagrangian relaxation, Benders' decomposition, knapsack problems, and matching and covering problems.

Discrete and continuous parameter Markov chains, Brownian motion, stationary processes.

Markov decision processes (stochastic dynamic programming): finite horizon, infinite horizon, discounted and average-cost criteria; reinforcement learning(RL): design and analysis of model-free, model-based, value-based, and policy-based RL algorithms, RL algorithms in continuous and discrete state and action space, and RL with functional approximation. These algorithms include but are not limited to (deep) Q-learning, asynchronous advantage actor-critic, soft actor-critic, and proximal policy optimization.

Introduction to time series: exploratory analysis, time-domain analysis and ARMA models, Fourier analysis, state space analysis. Introduction to multivariate analysis: principal components, canonical correlation, classification and clustering, dimension reduction.

Bayes procedures for estimation and testing. Minimax procedures. Unbiased estimators. Unbiased tests and similar tests. Invariant procedures. Sufficient statistics. Confidence sets. Large sample theory. Statistical decision theory.

Bayes factors, empirical Bayes theory, applications of generalized linear models.

Application of statistics to real problems presented by researchers from the University and local companies and institutes. (Taught over two semesters for a total of 3 credits.)

This is a graduate course on statistical machine learning.

Survey of literature in operations research and systems analysis.

Topics may include polynomial algorithms, computational complexity, matching and matroid problems, and the traveling salesman problem.

Advanced topics such as interior point methods, parallel algorithms, branch and cut methods, and subgradient optimization.

Advanced theoretic course, covering topics selected from weak convergence theory, central limit theorems, laws of large numbers, stable laws, infinitely divisible laws, random walks, martingales.

Advanced theoretic course including topics selected from foundations of stochastic processes, renewal processes, Markov processes, martingales, point processes.

This course covers both mathematical theory and statistical methodology concerned with extreme values in sequences of random variables. IID theory: the three types of extreme value distributions, statistical methods by block maxima and threshold exceedances. Extensions to dependent stochastic sequences: the extremal index and related concepts. Multivariate and spatial extremes, max-stable process. Applications in: engineering and strength of materials; finance and insurance; environment and climate.

Random measures and point processes on general spaces, Poisson and related processes, regularity, compounding. Point processes on the real line stationarity, Palm distributions, Palm-Khintchine formulae. Convergence and related topics.

Brownian motion, semimartingale theory, stochastic integrals, stochastic differential equations, diffusions, Girsanov's theorem, connections with elliptic PDE, Feynman-Kac formula. Applications: mathematical finance, stochastic networks, biological modeling.

Asymptotically efficient estimators; maximum likelihood estimators. Asymptotically optimal tests; likelihood ratio tests.

Convex analysis and optimization including sets, functions, basic concepts, minimax theory, duality, and optimality conditions.

Object Oriented Data Analysis (OODA) is the statistical analysis of populations of complex objects. Examples include data sets where the data points could be curves, images, shapes, movies, or tree structured objects.

Permission of the instructor.

Permission of the instructor.

Permission of the instructor.

Advance topics in current research in statistics and operations research.

Advanced topics in current research in statistics and operations research. This course is held at SAMSI.

Students will read selected works under supervision of instructor, and attend discussion meetings. Permission of the instructor.

Permission of the instructor.

Permission of the instructor.

Students work with other organizations (Industrial/Governmental) to gain practical experience in Statistics and Operations Research.

Permission of instructor.

Permission of instructor.