Monte Carlo methods are used in many application areas, including: finance, bioinformatics, computer graphics, discrete event simulation, physics, and statistical inference. Regarding graphics, there have been at least two technical Oscars awarded for Monte Carlo methods and one for quasi-Monte Carlo. This is a course on Monte Carlo as its own subject, so the application areas are used to motivate the ideas of Monte Carlo.
We will cover a broad selection of topics, touching on some applications, and on recent developments in Markov chain Monte Carlo and quasi-Monte Carlo.
Here is a list of topics. Last time we were able to cover almost all of them. The online text is more developed than last time. So I plan to bring in more advanced material. If time permits I will add some sequential Monte Carlo.
Monte Carlo methods are used in almost every branch of science and engineering. The topics that are most important are .... the ones that help you solve your problems. This varies from person to person. I've selected topics ranging from fundamental, that almost everybody needs a little, to specialized that some people will need a lot. In past years, the students have come from: statistics, computer science (graphics, machine learning, information retrieval), finance, biology, education, aero-astro, in the recent past.
- Art Owen
- Sequoia Hall 130
- My userid is owen on stanford.edu
- Office hour: Tuesday 1:30-2:30
The class text is one I'm writing. The first chapters are here. I will add some more as needed.
More references appear here. (A few links are broken at present.)
The homework will involve a mix of programming assignments using Monte Carlo and theoretical exercises. The mix is tilted towards applying Monte Carlo. Most students solve the problems with R or MATLAB, whichever they are most fluent with. You can use python or Mathematica or Julia or C++ or other tools (no spreadsheets though).
In class, closed to all notes, February 19. Questions on the midterm are different from homework questions (and, unsurprisingly, vice versa). They emphasize proofs, derivations, choices and insights.
The last homework will involve a project. The project may involve theory or methods or applications.Even if you are taking the class pass / no credit, you are still expected to do all of the problem sets, including the project, and to take the midterm.
Be sure to give Axess a working email address:
I expect to send a small number of important emails about the problem sets to the class via Axess. Most other announcements will be made in class. Also make sure to put stat 362 in the subject line of emails. Otherwise your email won't come to the top when I search for course related emails and I might not see it until end of quarter.Late penalties apply:
The assigned homework is due at Gradescope one second after 11:59:59pm on the assigned day. After that it is a day late. Each additional 24 hours that pass without it being uploaded make it another day late. Each day late is penalized by 10% of the homework's value. Homework more than 4 days late will ordinarily get 0.
To allow for sickness, interviews and other events, up to 3 days of late work are forgiven at the end of the quarter. (Work late enough to get zero does not get redeemed though.)