Instructor Information

Carsten Botts

Work Phone: 443-778-6993

Course Information

Course Description

This course is an introduction to fundamental tools in designing, conducting, and interpreting Monte Carlo simulations. Emphasis is on generic principles that are widely applicable in simulation, as opposed to detailed discussion of specific applications and/or software packages. At the completion of this course, it is expected that students will have the insight and understanding to critically evaluate or use many state-of-the-art methods in simulation. Topics covered include random number generation, simulation of Brownian motion and stochastic differential equations, output analysis for Monte Carlo simulations, variance reduction, Markov chain Monte Carlo, simulation-based estimation for dynamical (state-space) models, and, time permitting, sensitivity analysis and simulation-based optimization. Course Note(s): This course serves as a complement to the 700-level course EN.625.744 Modeling, Simulation, and Monte Carlo. EN.625.633 Monte Carlo Methods and EN.625.744 emphasize different topics, and EN.625.744 is taught at a slightly more advanced level. EN.625.633 includes topics not covered in EN.625.744 such as simulation of Brownian motion and stochastic differential equations, general output analysis for Monte Carlo simulations, and general variance reduction. EN.625.744 includes greater emphasis on generic modeling issues (bias-variance tradeoff, etc.), simulation-based optimization of real-world processes, and optimal input selection.

Prerequisites

Linear algebra and a graduate-level statistics course such as EN.625.603 Statistical Methods and Data Analysis.

Course Goal

To develop a theoretical and practical understanding of how Monte Carlo methods work and can be used.  

Course Objectives

  • By the end of the course, students should be able to:
    Use Monte Carlo methods to solve a myriad of practical problems.
  • By the end of the course, students should be able to:
    Explain the theoretical underpinnings of certain Monte Carlo methods.

When This Course is Typically Offered

Syllabus

  • Random Number Generation
  • Stochastic Differential Equations (Brownian Motion)
  • Bootstrap and Jacknife
  • Variance Reduction
  • Markov Chain Monte Carlo Methods
  • Kalman Filtering

Student Assessment Criteria

Homework 40%
Possibly (3) Exams 60%

Computer and Technical Requirements

Some (minor) computer programming will be required.    The coding examples given in class will be done in R.

Textbooks

Textbook information for this course is available online through the MBS Direct Virtual Bookstore.

Course Notes

There are no notes for this course.

(Last Modified: 01/12/2017 04:05:35 PM)