Ph.D. courses are an important part of the Ph.D. program in Decision Sciences. Our faculty regularly teach Ph.D. courses, most of them are currently offered once every two years. (See list below.) In addition to the courses offered by Decision Sciences faculty, our Ph.D. students also take a wide range of courses offered by other areas of the Fuqua School of Business and other departments of Duke University, such as Departments of Computer Science, Economics, Mathematics, and Statistics. Ph.D. students are encouraged and mentored to take the courses that match their specific research interest. A typical Ph.D. coursework provides a foundation that spans over decision theory, operations research, optimization and probability.

**BA 910, Bayesian Inference and Decision.** Methods of Bayesian inference and statistical decision theory, with emphasis on the general approach of modeling inferential and decision-making problems as well as the development of specific procedures for certain classes of problems. Topics include subjective probability, evaluation and assessment of probabilities, Bayesian inference and prediction, comparisons with classical methods, value of information, sequential decision making, and Bayesian game theory. (Taught by Bob Winkler)

**BA 911, Convex Optimization. **This course provides an in-depth treatment of convex optimization, with a particular emphasis on duality. Linear programming is covered in detail. Motivating applications from finance, operations, engineering, and economics are explored. (Taught by Ali Makhdoumi)

**BA 912, Dynamic Programming and Optimal Control.** This course covers the basic models and solution techniques for problems of sequential decision making under uncertainty. We introduce discrete and continues time models with finite and infinite planning horizon. Applications are drawn from economics, finance, operations and engineering. (Taught by Peng Sun)

**BA 913, Choice Theory.** This course deals with advanced topics in choice theory, with emphasis on rational choice and the interface between decision theory, game theory, theories of markets, and social choice theory. The goal is to acquaint students with historical developments as well as recent advances in choice theory and to equip students that can be used in a wide variety of social science applications. (Taught by Bob Nau)

**BA 915, Stochastic Models**. This course is an introduction to the theory of stochastic processes. The course begins with a review of probability theory and then covers Poisson processes, discrete-time Markov chains, martingales, continuous-time Markov chains, and renewal processes. The course also focuses on applications in operations research, finance, and engineering. No prior knowledge of measure theory is required. However, the focus of the course is on the mathematics and proofs are emphasized. Prerequisites: at least a one-semester calculus-based course in probability. A background in real analysis is helpful. (Taught by Alessandro Arlotto, cross-listed as MATH742 and STA715.)

**BA 991, Statistical Inference on Graphs**. An emerging research thread in statistics and machine learning deals with finding latent structures from data represented by graphs or matrices. This course will provide an introduction to mathematical and algorithmic tools for studying such problems. We will discuss information-theoretic methods for determining the fundamental limits, as well as methodologies for attaining these limits, including spectral methods, semidefinite programming relaxations,

Linear/quadratic programming relaxations, message passing (belief propagation) algorithms, etc. Specific topics will include spectral clustering, planted clique and partition problem, community detection on stochastic block models, hidden Hamiltonian cycle problem, planted bipartite graph matching problem, noisy graph isomorphism, and statistical-computational tradeoffs. Prerequisites: Maturity with probability theory and linear algebra. Familiarity with statistical theory, optimization, and algorithms. (Taught by Jiaming Xu.)