1 Decision Sciences Department COURSE NUMBER: DNSC 6206 (Fall 2020) COURSE TITLE: Stochastic Foundations: Probability Models COURSE DESCRIPTION: This course introduces the foundations of Probability, along with the commonly used Probability models (Binomial, Normal, and Poisson) in predictive analytics. Topics covered include probability laws, probability models for modeling dependence, univariate and bivariate models and their applications, conditional mean models including simple regression and extensions to probit and logit models and classification models. COURSE PRE-REQS: MSBA Program Candidacy or instructor approval. PROFESSORS: Refik Soyer, Professor of Decision Sciences and of Statistics Office: Funger Hall, 415 B Phone: 202-994-6445 E-mail:
[email protected] Office Hours: TBA TEXTBOOKS: Probability and Statistics, 4th Edition M. H. DeGroot and M. J. Schervish (Strongly Recommended) Addison-Wesley, 2012, ISBN: 978-0-321-50046-5 COURSE OBJECTIVES: To provide students with an understanding of • Key probability concepts and graphical representations • The basic probability models and related probability distributions (normal, binomial, and Poisson) • Commonly used measures for univariate and bivariate distributions (means, variances, co-variances) • Conditional mean models, regression and classification models and their applications. SOFTWARE: The course will primarily involve using R. 2 COURSE SCHEDULE Session Date Subject/Topic Readings 1 Dealing with uncertainty. Interpretations of probability. Concept of a random experiment. Special random quantities: Events and random variables. Bernoulli trials and categorical random variables. Introduction to rules of probability. Defining conditional probability. DeGroot & Schervish (DS) Ch. 1.1-1.10, Ch. 2.1 2 Concept of dependence. Conditional probability and dependence. Categorical random variables and contingency table models. Law of total probability and Bayes’ rule. Graphical representations for probability models: trees for probability computations and graphical models for describing dependence. DS Ch. 2.1-2.3 3-4 Random variables (RVs): Discrete RVs and univariate and multivariate probability distributions. Probability mass and density functions. Cumulative distributions. Means and variances for random variables. Covariance of random variables. Conditional means and variances. DS Ch. 3.1-3.6 (Discrete RVs part) Ch. 4.1-4.7 (Discrete RVs part) 4-5 Commonly used univariate probability models (Discrete RVs). Binomial, Geometric, Poisson, and Multinomial. Applications. DS Ch. 5.1-5.5 and Ch. 5.9 5-6 Introduction to continuous RVs: Uniform, exponential, gamma, normal and bivariate normal probability models. Applications. DS Ch. 3.2-3.3 Ch. 4.1-4.3, 4.6- 4.7 Ch. 5.6-5.7, 5.10 7 Regression and classification models. Conditional mean and introduction to normal regression model. Logit, probit and other classification models. Applications. DS Ch. 4.7, DS Ch. DS Ch. 11.1-11.2 (up to page 702). 8 Final Exam October 21, 2020 3 ASSIGNMENT OF CREDIT HOUR POLICY: Students will spend about 2 hours per week in online sessions. Required readings, videos and assignments for the course are expected to average 8 hours per week. All online sessions during the regular class time (W 4:30 -7:00 pm) will be recorded. There will be additional on-line sessions scheduled for students who will participate from abroad. Students are expected to attend the online sessions 1) having read the material for the current lecture; 2) having watched pre-session recordings; 3) having reviewed the material of the previous lectures. WEEKLY PROBLEM/REVIEW SESSIONS: There will be problem/review sessions on Fridays 4:00-5:30 pm starting on September 11th. These sessions will be recorded and recordings will be posted as soon as they become available. Attendance to the problem/review sessions are voluntary. The sessions will be taught by doctoral students. An additional review session will be scheduled for students who will participate from abroad. GRADING: The course grade will be based on group homework assignments, quizzes, and a final examination according to the following weights: Quizzes: 30%. Homework assignments (Group effort): 30%. Final exam: 40%. Quizzes There will be three on-line quizzes. They will be based on current and prior assigned readings and material covered in the class sessions. Homework Assignments Homework assignments will typically require the use of software. A typical homework assignment will consist of a few problems with several parts. Solutions will be posted on the course web site. These are group efforts. The groups will consist of 2 OR 3 students and will be determined by the second session. Assignments will be available by Thursday night every week and they will due on the Saturday of the following week by 12:00 noon. For example, the assignment 1 will be posted on Thursday September 3rd and it will be due on Saturday September 12th by 12:00 noon. No late homework assignments will be accepted. Submission guidelines for homework assignments In preparing the submissions, please follow these guidelines: Make sure the solutions are typed or easily readable by anyone; Ensure a clear logical flow and mark your answers; Include names of your group members on the first page. Final Exam The final exam is individual and is scheduled for Wednesday October 21st. 4 EXAM, QUIZZES AND HOMEWORK ASSIGNMENTS SCHEDULE: The assignment schedule is tentative and might be adjusted. Name Due Date (tentative) Quiz 1 Session 3 Quiz 2 Session 5 Quiz 3 Session 7 HW 1 Saturday, September 12 HW 2 Saturday, September 19 HW 3 Saturday, September 26 HW 4 Saturday, October 3 HW 5 Saturday, October 10 HW 6 Saturday, October 17 Final Exam Week 8: Wednesday, October 21st. ACADEMIC INTEGRITY: Cheating and plagiarism will not be tolerated. Any case will automatically result in loss of all the points for the assignment, and may be a reason for a failing grade and/or grounds for dismissal. In case of a group assignment, all group members will receive a zero grade. Any suspected case of cheating or plagiarism or behavior in violation of the rules of this course will be reported to the Office of Academic Integrity. Students are expected to know and understand all college policies, especially the code of academic integrity available at: http://www.gwu.edu/~ntegrity/code.html DISABILITY SERVICES: Any student who may need an accommodation based on the impact of a disability should contact the Office of Disability Support Services (DSS) to inquire about the documentation necessary to establish eligibility, and to coordinate a plan of reasonable and appropriate accommodations. DSS is located in Rome Hall, Suite 102. For additional information, please call DSS at 202-994-8250, or consult www.disabilitysupport.gwu.edu. 5 ATTENDANCE: The George Washington University Bulletin, Graduate Programs, 2009–2010: "Regular attendance is expected. Students may be dropped from any class for undue absence…. Students are held responsible for all of the work of the courses in which they are registered, and all absences must be excused by the instructor before provision is made to make up the work missed." CHANGES: The instructors reserves the right to make revisions to any item on this syllabus, including, but not limited to any class policy, course outline and schedule, grading policy, tests, etc. Note that the requirements for deliverables may be clarified and expanded in class, via email, or on Blackboard. Students are expected to complete the deliverables incorporating such additions and to check email and Blackboard announcements frequently.
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