IEORE4101 Probability Models (Management Science and Engineering)
(3 credits) Imagine yourself as an Amazon department manager who needs to decide how to stock up products at various distribution centers, knowing that demands will be uncertain. Or imagine yourself as a Goldman Sachs trader who needs to decide how to trade commodities, subject to fluctuating commodity prices. You have access to historical data, from which you may predict to certain degree the future, but you also know that the future is full of uncertainty. How can you make scientifically sound decisions in these situations?
This course is about making sense of data and uncertainty. We will learn how to understand data, visualize data, come up with sound statistical models of data, and reason probabilistically about these models. The mathematical content will be at a level that is comparable to IEOR 4150, but the approach will be more hands-on, and the topics will be illustrated through numerous business examples.
Syllabus and Topics:
• Probability: Discrete and continuous distributions, independence and conditioning, Bayes’ rule, expectation and variance, law of large numbers, central limit theorem, extremal value theory
• Simulation: Monte Carlo simulation, inverse transform method, acceptance/rejection method
• Statistics: Interval estimation and output analysis of simulated data, hypothesis testing, regression
• Miscellaneous topics: descriptive statistics, data visualization, psychology of decision making under uncertainty.
Pre-requisites: Restricted to students in the Management Science and Engineering (MSE) MS Program. Understanding of single and multi variable calculus. Basic understanding of optimization theory is also desired though not required.