625.744.8VL - Modeling, Simulation, and Monte Carlo

Course Structure

Course Structure:

Each session material will be presented in a virtual-live lecture/discussion on Zoom. Recordings of the lectures will be posted in the corresponding session's module folder. Homework assignments will also be posted there.

Course Topics

• General issues in simulation; math review (Appendix A)

• Statistics review (Appendix B); model building: bias-variance tradeoff

• Probability review (Appendix C); model building: model selection; Fisher information matrix

• Model Fitting; introduction to random number generation (Appendix D)

• Random number generation (Appendix D continued) and variance reduction for simulation output

• Stochastic simulations; continuous stochastic optimization methods; brief introduction to stochastic approximation

• Simulation-based optimization for continuous optimization; common random numbers in simulation optimization

• Simulation-based optimization for continuous optimization (continued)

• Markov processes (Appendix E); discrete stochastic optimization methods and simulation- based optimization

• Discrete stochastic simulation-optimization (continued); simulation-optimization case study

• Markov chain Monte Carlo (MCMC)

• Input selection, factorial design, and optimal experimental design

• Input selection and optimal experimental design (continued)

• Final projects

Course Goals

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 Learning Outcomes (CLOs)

• Review and discuss some of the most important principles and algorithms for simulation and Monte Carlo methods.
• 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. (It is not the intention of the class to dwell on the details of any specific application; students will be expected to make the links to their applications of interest).

Textbooks

“Introduction to Stochastic Search and Optimization,” J. C. Spall, Wiley, 2003, ISBN: 0-471-33052-3 (website: www.jhuapl.edu/ISSO). Students are strongly encouraged to bring the textbook to class sessions.

Required Software

Some homework assignments will require the use of a computer; students are free to use any programming language with they are comfortable, but may find it easier to complete the homework with the use of MATLAB (the website for the textbook includes some MATLAB code).

Student Coursework Requirements

The grade for the course will be based on a combination of performance on the homework/quizzes and the final project. Homework will be assigned most weeks and will be due the following class. One or more problems will be selected for grading. However, all problems will be reviewed for completeness.

The grade is assigned according to the proportions: Homework/quizzes: 70% (Homework will be reviewed by the grader and the instructor.) Final project: 30% (combination of proposal and final written report).

Final Project

A final written report is required on a subject of relevance to the course. A brief (one- to two-page) project proposal is required shortly after the week 11 class session. Details such as length and scope of the paper, and due date  will be given later.

Grading Policy

Grades will be assigned on an absolute scale (not a curve):

Course Policies

Homework:
Homework, when assigned, will be due at the next class session unless notified otherwise. The exercises will include hand (“pencil and paper”) problems and computer-based assignments (for computational exercises, students are encouraged to turn in code or other supplementary information in case there are questions about the main results being presented; all such information should be clearly labeled). Work submitted for a grade is expected to be the student’s own work.

Late Homework:
All homework is due as assigned. An assignment handed in one week late will be given half credit; after one week, no credit. Exceptions to the late policy will be made on a case-by-case basis; the student must contact the instructor in advance in such a case.

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 theory underlying aspects of simulation and Monte Carlo, not high-level architecture, user interface, software design, etc. Further, to facilitate general understanding and interest, the class will not focus on any one particular application area; students are expected to make their own connections of the material in the class to their specific application areas of interest. It is recommended that this course only be taken in the last half of a student’s degree program..

Academic Policies

Deadlines for Adding, Dropping and Withdrawing from Courses

Students may add a course up to one week after the start of the term for that particular course. Students may drop courses according to the drop deadlines outlined in the EP academic calendar (https://ep.jhu.edu/student-services/academic-calendar/). Between the 6th week of the class and prior to the final withdrawal deadline, a student may withdraw from a course with a W on their academic record. A record of the course will remain on the academic record with a W appearing in the grade column to indicate that the student registered and withdrew from the course.

Academic Misconduct Policy

All students are required to read, know, and comply with the Johns Hopkins University Krieger School of Arts and Sciences (KSAS) / Whiting School of Engineering (WSE) Procedures for Handling Allegations of Misconduct by Full-Time and Part-Time Graduate Students.

This policy prohibits academic misconduct, including but not limited to the following: cheating or facilitating cheating; plagiarism; reuse of assignments; unauthorized collaboration; alteration of graded assignments; and unfair competition. Course materials (old assignments, texts, or examinations, etc.) should not be shared unless authorized by the course instructor. Any questions related to this policy should be directed to EP’s academic integrity officer at ep-academic-integrity@jhu.edu.

Students with Disabilities - Accommodations and Accessibility

Johns Hopkins University values diversity and inclusion. We are committed to providing welcoming, equitable, and accessible educational experiences for all students. Students with disabilities (including those with psychological conditions, medical conditions and temporary disabilities) can request accommodations for this course by providing an Accommodation Letter issued by Student Disability Services (SDS). Please request accommodations for this course as early as possible to provide time for effective communication and arrangements.

For further information or to start the process of requesting accommodations, please contact Student Disability Services at Engineering for Professionals, ep-disability-svcs@jhu.edu.

Student Conduct Code

The fundamental purpose of the JHU regulation of student conduct is to promote and to protect the health, safety, welfare, property, and rights of all members of the University community as well as to promote the orderly operation of the University and to safeguard its property and facilities. As members of the University community, students accept certain responsibilities which support the educational mission and create an environment in which all students are afforded the same opportunity to succeed academically. 

For a full description of the code please visit the following website: https://studentaffairs.jhu.edu/policies-guidelines/student-code/

Classroom Climate

JHU is committed to creating a classroom environment that values the diversity of experiences and perspectives that all students bring. Everyone has the right to be treated with dignity and respect. Fostering an inclusive climate is important. Research and experience show that students who interact with peers who are different from themselves learn new things and experience tangible educational outcomes. At no time in this learning process should someone be singled out or treated unequally on the basis of any seen or unseen part of their identity. 
 
If you have concerns in this course about harassment, discrimination, or any unequal treatment, or if you seek accommodations or resources, please reach out to the course instructor directly. Reporting will never impact your course grade. You may also share concerns with your program chair, the Assistant Dean for Diversity and Inclusion, or the Office of Institutional Equity. In handling reports, people will protect your privacy as much as possible, but faculty and staff are required to officially report information for some cases (e.g. sexual harassment).

Course Auditing

When a student enrolls in an EP course with “audit” status, the student must reach an understanding with the instructor as to what is required to earn the “audit.” If the student does not meet those expectations, the instructor must notify the EP Registration Team [EP-Registration@exchange.johnshopkins.edu] in order for the student to be retroactively dropped or withdrawn from the course (depending on when the "audit" was requested and in accordance with EP registration deadlines). All lecture content will remain accessible to auditing students, but access to all other course material is left to the discretion of the instructor.