625.744 - Simulation and Monte Carlo Methods Course Homepage
Instructor Information
James Spall
Email: james.spall@jhuapl.eduWork Phone: (443) 778-4960
James C. Spall is a member of the Principal Professional Staff at the JHU Applied Physics Laboratory, is the Chair of the Applied and Computational Mathematics Program within the JHU School of Engineering, and is a Research Professor in the JHU Department of Applied Mathematics and Statistics. Dr. Spall has published extensively in the areas of control and statistics (including two books) and holds two U.S. patents for inventions in control systems. Among other appointments, he was the Program Chair for the 2007 IEEE Conference on Decision and Control and is a Senior Editor for the IEEE Transactions on Automatic Control and Contributing Editor for the Current Index to Statistics. Dr. Spall has received numerous research and publications awards and is a Fellow of IEEE, a member of the American Statistical Association, and a Fellow of the engineering honor society Tau Beta Pi. He won the EP Excellence in Teaching Award in 2006. Click here for Web site with additional publications (and other) information.
Course Information
Course Description
Computer simulation and related Monte Carlo methods are widely used in engineering, scientific, and other work. Simulation provides a powerful tool for the analysis of real-world systems when the system is not amenable to traditional analytical approaches. In fact, recent advances in hardware, software, and user interfaces have made simulation a "first line" method of attack for a growing number of problems. Areas where simulation-based approaches have emerged as indispensable include decision aiding, prototype development, performance prediction, scheduling, and computer-based personnel training. This course introduces concepts and statistical techniques that are critical to constructing and analyzing effective simulations, and discusses certain applications for simulation and Monte Carlo methods. Topics include random number generation, simulation-based optimization, model building, bias-variance tradeoff, input selection using experimental design, Markov chain Monte Carlo (MCMC), and numerical integration.
Prerequisites
Multivariate calculus, familiarity with basic matrix algebra, graduate course in probability and statistics (such as 625.403). Some computer-based homework assignments will be given. It is recommended that this course only be taken in the last half of a student's degree program
Course Goal
This course introduces fundamental issues in simulation-based analysis and Monte Carlo-based computing. The emphasis will be on rigorous analysis and interpretation and an objective treatment of various approaches. The advantages and disadvantages of various methods will be discussed.
Course Objectives
- Review and discuss some of the most important principles and algorithms for simulation and Monte Carlo methods. The course will cover most of the material in the Appendices and Chapters 12 to 17 of the textbook (book information is at http://www.jhuapl.edu/ISSO). Note that Chapters 12 to 17 of the textbook can largely be studied without covering the earlier chapters in the book; a small amount of material from the earlier chapters will be covered as needed.
- Recognize key limitations and assumptions associated with popular methods in simulation and Monte Carlo.
- Discuss the relationships among methods and algorithms and provide some guidance about which algorithms are appropriate for which problems.
- Provide the background to implement the algorithms and/or critically evaluate the implementations of others in a wide variety of practical problems (but it is not the intention of the class to dwell on the details of any specific application; the student will be expected to make the link to his/her applications of interest).
When This Course is Typically Offered
Fall semester, odd years, at the Applied Physics Laboratory.
Syllabus
Topics Covered
- General issues in simulation; brief math review
- Model building; bias-variance tradeoff; brief statistics review
- Model building; model selection; brief probability review
- Model building; model selection; Fisher information matrix
- Model fitting via regularization; introduction to random number generation
- Random number generation (continued) and variance reduction for simulation output
- Stochastic timed discrete-event systems and simulations; brief introduction to SPSA
- Simulation-based optimization by gradient-free methods (FDSA and SPSA); common random numbers
- Simulation-based optimization by gradient-based methods (IPA, LR, and sample path)
- Markov chain Monte Carlo
- Input selection and optimal experimental design for linear models
- Input selection and optimal experimental design for nonlinear models
- Statistical methods for selecting the best option using simulation runs
- Class presentations of final projects
Student Assessment Criteria
| Homework | 65% |
| Final project | 30% |
| Discussant on other project | 5% |
The above list of topics and grading criteria are tentative; the final versions will be provided in the course syllabus to be handed out on the first day of class (any changes relative to the information above are likely to be small).
Computer and Technical Requirements
Some homework assignments will require the use of a computer; the student is free to use any programming language with which he/she is comfortable, but may find it easier to complete the homework if he/she uses MATLAB (the book's Web site includes some MATLAB code).
Participation Expectations
Homework will be assigned on a weekly basis and will be due the following class. The homework exercises will include hand ("pencil and paper") problems and computer-based assignments. Unless notified otherwise, students are required to work independently on the homework.
Textbooks
Textbook information for this course is available online through the MBS Direct Virtual Bookstore.
Course Notes
There are no notes for this course.
Final Words from the Instructor
Students should come into the class with a good working knowledge of probability and statistics at the beginning graduate level (at least at the level of 625.403) and knowledge of multivariate calculus and basic matrix algebra. This class focuses on the mathematical aspects of simulation and Monte Carlo, as opposed to the high-level architecture, user interface, software design, etc. aspects. Further, to facilitate general understanding and interest, the class will not focus on any one application area; students are expected to make their own connections of the material in the class to their specific applications of interest. It is recommended that this course only be taken in the last half of a student's degree program.
(Last Modified: 07-13-2009 at 4:40:40 PM)