Doctoral area of specialization in Decision Sciences
The doctoral area of specialization in Decision Sciences typically requires five doctoral level courses as part of the student's plan of study. These are in addition to the appropriate breadth and foundation courses and the appropriate methodology courses required by the Ph. D. program. In particular cases, some of the five doctoral area courses may be from allied fields such as Economics, Information Systems, Operations Research, and Statistics, offered by other departments at GWU or one of the consortium universities.
DNSC 397: Decision Analysis
Topics in decision analysis. Topics include decision theory, value of information, utility theory, modeling attitude towards risk, risk management, multi-criteria decision making paradigms, Bayesian statistics, game theory, and strategic decision making. Graphical models and decision structuring tools such as decision trees, influence diagrams and hierarchies are presented and model building aspects are emphasized.
DNSC 397: Deterministic Optimization Models and Algorithms
The course provides a thorough introduction to modeling and solving deterministic decision problems using optimization techniques. Applications covered span the fields of operations, management, planning, transportation, finance and economics. Topics include: Linear Programming, the Simplex Method, the Interior Point Method, Duality and Sensitivity, Multiobjective and Goal Programming, and Deterministic Dynamic Programming. The course emphasizes both theory and application, has a strong computer orientation and makes use of commercial software for solving realistic problems.
DNSC 397: Stochastic Modeling and Programming
This course will focus on Stochastic Modeling and Programming. Stochastic Programming is a discipline intersecting with probability theory and statistics on one hand and with mathematical programming on the other hand. It is a framework for modeling optimization problems that involve uncertainty. While deterministic optimization problems are formulated with known parameters, real world problems almost invariably include some unknown ones; their eventual outcome depends on the future realization of random events. Stochastic Programming relies upon the fact that probability distributions governing the data are known or can be estimated. The goal here is to find some policy that is feasible for (almost) all possible realizations and optimizes a function of the decision and the random variables. More generally, such models are formulated, analytically or numerically solved, and studied in order to provide useful information to the decision-maker.
DNSC 328: Bayesian Statistics
This course is an introduction to Bayesian viewpoint in Statistics. There are no graduate-level prerequisites, but students are expected to be familiar with essential features of probability and statistical inference as usually covered in an introductory course in statistics. Basic components of the Bayesian viewpoint towards inference will be introduced and Bayesian analysis of standard statistical problems will be presented with comparisons with classical methods. Fundamental concepts such as Bayesian probability intervals, Bayesian hypothesis testing, model comparison and prediction will be introduced and implications of Bayesian view on research methodology will be discussed. Students will be introduced to the Bayesian computer package WinBUGS. Using WinBUGS Bayesian analyses of hierarchical (or multi-level) models, random effect models and logit/probit models will be discussed. Using real data, students will learn carrying out Bayesian analyses of complex models as well as interpreting and communicating the results.
DNSC 397: Game Theory
The purpose of this course is to acquaint the student with the conceptual foundations of game theory. We will also look at some of the more recent applications of game theory to problems in operations and information technology. Topics include: Utility and Expected Utility, Strategic Form Games and Dominance solvability, Nash Equilibrium and Applications, Mixed Strategies and Zero Sum games, Extensive Form Games, Repeated Games, Dynamic Games and Games with Incomplete Information.
DNSC 397: Applied Longitudinal Data Analysis
Focusing on the theoretical, logical and empirical underpinnings for studying change across time in human and organizational behavior, this course is centered around two distinct but related themes: specifying and testing longitudinal change models (including path analysis and structural equation modeling of change) and hierarchical linear modeling (particularly in the form of latent growth analysis). Both are topics which doctoral candidates are likely to actively encounter both in the course of their studies and following graduation. The sequencing of topics follows the influential textbook by Judith Singer and John Willett entitled "Applied Longitudinal Data Analysis". The course will involve a fair amount of *intellectual* investment and some, but not a lot of, computer work using basic SAS skills; a term paper will serve in lieu of a final examination. The level of effort will be substantially less than that of DNSC 274, although active participation in the class discussions will be expected. DNSC 274 (or equivalent, with the permission of the instructor) is the only prerequisite.
DNSC 397: Advanced Topics in Forecasting and Time Series Analysis
This course is designed as a continuation to the time-series models discussed in MGT 207 and FIN 271. Advanced models in time series analysis will be studied in the course. Fundamental concepts and methodologies will be introduced and their implementation to real data will be discussed. SAS software will be used for implementation of different methodologies. Topics include: multivariate time-series models such as transfer function (dynamic regression) models and multivariate ARMA processes, stochastic volatility models such as ARCH and GARCH models, multivariate stochastic volatility models, state-space models and Kalman filtering, Bayesian dynamic linear models and Bayesian forecasting. Prerequisites: MGT 207 or FIN 271 or an equivalent course.
DNSC 397: Logical and Empirical Bases for Establishing Cause: Confounding, Mediation, Suppression, and Moderation
This course focuses on the logical and empirical underpinnings of contemporary approaches for building and testing causal models, with particular emphasis on four commonly-encountered types of causal models: confounding models, mediator models, suppressor models, and moderator models. Each session's discussion will revolve around a number of readings drawn from the refereed literature and made available to all students via download from Blackboard. There will be periodic assignments requiring participants to apply the material we discuss in the class sessions. The course will involve a fair amount of *intellectual* investment and some, but not a lot of, computer work using basic SAS skills; a term paper will serve in lieu of a final examination. The level of effort will be substantially less than that of DNSC 274, although active participation in the class discussions will be expected. DNSC 274 (or equivalent, with the permission of the instructor) is the only prerequisite.
DNSC397: Network Flow Models
Network models for industrial logistics systems, transportation systems, communication systems, and other applications. Emphasizes a rigorous treatment of algorithms and their efficiency algorithms for shortest routes, maximum flows, minimum cost flows, traffic equilibrium, and network design. Implementation issues.
DNSC 397: Multiobjective Programming
An introduction to multiobjective decision making, classification of multiobjective programming methods; techniques for generating the efficient frontier, interactive techniques, goal programming, and their applications.
DNSC397: Integer Programming / Discrete Optimization
General and 0-1 Integer Programming: Formulations, LP relaxation, rounding, unimodularity. Implicit enumeration and branch-and-bound tecniques. Polyhedral description: vertices, feasibility, valid inequalities, faces and facets. Value function, surrogate, subadditive and Lagrangean duality. Cutting planes, Gomory's algorithm, Chvatal cuts, Lovasz-Schrijver cutting planes. Decomposition methods. Preprocessing techniques and heuristics.
DNSC 397: Financial Optimization
Optimization models play an increasingly important role in financial decisions. Many computational finance problems ranging from asset allocation to risk management, from option pricing to model calibration, can be solved efficiently using modern optimization techniques. This course discusses several classes of optimization models (including linear, quadratic, integer, dynamic, stochastic, conic and robust programming, discrete and continuous time stochastic processes) encountered in a financial context. This is an optimization course, the objective of which is to create a bridge between mathematical models and financial applications. Each class will be devoted to 1) the detailed description of an optimization technique and 2) the use of this latter for the modeling and solution of financial problems. Software packages (Matlab, AMPL) will be used.
DNSC 397: Numerical/Computational Methods
The course will be highly interactive with individual and group assignments and with intensive computer practice. The students will be offered various problems and projects to work on during the semester. Some of the projects will involve the use of certain software packages, while some others will require coding. In addition, each of the students will be required to solve homework assignments, mostly programming tasks. Grading will be based on homework and projects. The course concentrates on OR modeling and problem solving with AMPL, a mathematical modeling language. Additionally, elements of other programming environments will be described, and a few assignments will be given, in particular, in PERL to realize basic data structures and combinatorial algorithms; in C++ to develop basic routines, and interface with CPLEX.
DNSC397: Nonlinear Programming
Introduction to methods for obtaining approximate solutions to unconstrained and constrained minimization problems of moderate size. Emphasis on geometrical interpretation and actual coordinate descent, steepest descent, Newton and quasi-Newton methods, conjugate gradient search, gradient projection and penalty function methods for constrained problems. Specialized problems and algorithms treated as time permits.
STAT 273: Stochastic Processes
Fundamental notions of Markov chains and processes, generating functions, recurrence, limit theorems, random walks, Poisson processes, birth and death processes, applications. Prerequisite: Stat 201-2.
Other Recommended Courses:
DNSC 275: Advanced Statistical Modeling and Analysis
Advanced topics associated with the general linear model. Testing for and remediation of assumption violations. Detection of outliers, influential observations, and multicollinearity. Alternative design strategies in the analysis of variance; latent growth analysis; hierarchical linear modeling; testing for interactions and parallelism.
DNSC 276: Exploratory and Multivariate Data Analysis
Methods for exploratory and multivariate data analysis. Application and comparison of advanced multivariate analytical procedures. Multivariate and discriminant analysis, LISREL analysis, and canonical correlation.
DNSC 277: Applied Forecasting and Time-Series Analysis for Managers
Introduction to various forecasting techniques, including time-series regression models, cyclical trends, exponential smoothing methods, seasonal and nonseasonal ARIMA processes, and the Box-Jenkins approach. Application of forecasting methods in economics, finance, and marketing.
DNSC 279: Data Mining
Techniques that can be used to discover relationships in large data sets, including regression models, decision trees, neural networks, clustering, and association analysis.
EMSE 292: Dynamic Programming
The course is suitable for students who have prior exposure to probability. Basic knowledge of stochastic processes, Markov chains in particular, is recommended but not required since these topics will be reviewed in class. This course focuses on modeling and computing optimal solutions of sequential decision models under uncertainty that arise in many contexts, including operations and revenue management, finance, computer science, artificial intelligence, among others. Examples of such problems: when to exercise a stock option (optimal stopping), how many airplane reservations to offer to compensate for cancellations (overbooking/yield management), when and how many units to reorder (inventory control), if a request for service should be accepted or not (admission control), or should a robot continue its task or return to base (resource management). Dynamic programming (DP) offers a natural way to model sequential decision making problems under uncertainty, and provides the mathematical and algorithmic framework to analyze and solve these problems. Recent computational techniques, such as approximate dynamic programming, extend the applicability of DP models, and make it possible to solve large-scale problems.
Recommended Courses From other Fields:
STAT 201: Mathematical Statistics-I
Distribution theory, sampling theory, estimation, sufficient statistics, hypothesis testing, analysis of variance, multivariate normal distribution. Prerequisite: Math 33, 124. (Academic year)
STAT 202: Mathematical Statistics-II
Distribution theory, sampling theory, estimation, sufficient statistics, hypothesis testing, analysis of variance, multivariate normal distribution. Prerequisite: Math 33, 124. (Academic year)
STAT 215: Applied Multivariate Analysis-I
Application of multivariate statistical techniques to multidimensional research data from the behavioral, social, biological, medical, and physical sciences. Prerequisite: Stat 119, 157-58; Math 124. (Alternate academic years)
STAT 216: Applied Multivariate Analysis-II
Application of multivariate statistical techniques to multidimensional research data from the behavioral, social, biological, medical, and physical sciences. Prerequisite: Stat 119, 157-58; Math 124. (Alternate academic years)
STAT 271: Foundational and Philosophical Issues in Statistics
Axiomatic underpinnings of Bayesian statistics, including subjective probability, belief, utility, decision and games, likelihood principle, and stopping rules. Examples from legal, forensic, biological, and engineering sciences. Students are expected to have a background in computer science, economics, mathematics, or operations research. Prerequisite: Stat 201-2.
STAT 273: Stochastic Processes
Fundamental notions of Markov chains and processes, generating functions, recurrence, limit theorems, random walks, Poisson processes, birth and death processes, applications. Prerequisite: Stat 201-2. (Alternate academic years)
STAT 289: Reliability And Risk Analysis
The methods of reliability, life testing an d survival analysis, provide an essential technology for risk analysis. The aim of this course is to provide an overview of this technology from a modern perspective, a perspective that encompasses many recent developments. These are to be summarized in a book that the instructor is developing and the course will be based on the material therein. Topics to be covered will be: an overview of the Bayesian paradigm for uncertainty quantification, exchangeability and its role in life testing and failure modeling, univariate and multivariate models for desc ribing the failure of units and systems, interdependent (causal and cascad ing failures), life testing and information in life tests, the elicitation, codification and modulation of expert testimonies in reliability, sign ature analysis in survival data analysis, dynamic environments and the ro le of stochastic process models for competing risks, degradation modeling and failures characterized by multiple scales. The course will conclude with a discussion of the relevance of the above material to financial mathematics and financial risk analysis.The course material should be of interest to those in risk analysis, in engineering reliability, biostatistics and survival analysis, quality control analysts, economists and those in mathematical finance. Prerequisites: Some background in probability and statistics and mathematical maturity.
EMSE 208: Stochastic Foundations of Operations Research
Topics in probability theory, stochastic processes, and statistical inference. Foundations of probability, conditional probability and expectation, Poisson processes, Markov chains, and Brownian motion. Prerequisite: ApSc 116 or permission of instructor. (Fall)
ECON 275: Econometrics-I
Statistical foundations for econometrics; standard methods of estimation and inference for classical and generalized regression models. Same as Stat 275. (Fall)
ECON 276: Econometrics-II
Topics may include asymptotic theory, statistical endogeneity, instrumental variables estimation, discrete and limited dependent variable models, and time-series models. Prerequisite: Econ 375. Same as Stat 276. (Spring)
ECON 277: Econometrics-III
Econometric methods for systems of equations and panel data, with additional topics that may vary from year to year. Prerequisite: Econ 376.