Opening Statements on Markov Chain Monte Carlo

This quarter I am TAing UCLA’s Statistics 102C. Introduction to Monte Carlo Methods for Professor Qing Zhou. This course did not exist when I was an undergraduate, and I think it is pretty rare to teach Monte Carlo (minus the bootstrap if you count that) or MCMC to undergrads. I am excited about this class because to me, MCMC turns Statistics on its head. It felt like a totally different paradigm compared to the regression and data analysis paradigm that I was used to at the time. It also exposes students to the connection between Statistics/MCMC and other fields such as Computer Science, Genetics/Biology, etc.

I usually do not have much to talk about during week 1, especially if my class is the second day of the quarter. Today was an exception because I wanted to excite the class about this topic.

Some examples I discussed:

• the general recipe for Monte Carlo methods
• the bootstrap as an example of resampling, and R loops
• computing and mention of Buffon’s Needle
• scheduling/timetabling and occupancy/matching problems using stochastic search (simulated annealing, Tabu search etc.)
• mention of genetic algorithms and swarm intelligence
• PageRank as a Markov process
• drawing a random sample of web pages using Random Walk Metropolis-Hastings
• short inventory of fields and situations where MCMC is popular

You can see my handout here.