Stat/Math 523

Advanced Theory of Probability

Instructor

• Peter Hoff
• C-319 Padelford
• 221-6982
• hoff@stat.washington.edu

Times and Places

• Lecture: MWF 11:30-12:20, Padelford C-301.
• Office hours: M 9:30-11:30, W 10:30-11:30, and by appointment
• Class homepage : http://www.stat.duke.edu/~pdh10/Teaching/stat523

Course Materials

• "Probability: Theory and Examples", Durrett (1995) typo list;
• journal articles;
• additional material will be made available as the quarter progresses.

• Markov chains:
  • 5.1-5.5 of Durrett.
• Ergodic theorems:
  • 6.1-6.5 of Durrett;
  • additional material on Markov chain Monte Carlo;
  • additional material on entropy and exponential families.
• Brownian motion:
  • 7.1-7.6, 7.8 of Durrett intersected with material not covered in 522.
• Exchangeability:
  • de Finetti's theorem and Bayes rule;
  • exchangeability for arrays.
• Measures on measures:
  • Polya's urn and the Dirichlet distribution;
  • Doob's theorem, topologies for spaces of measures, and Schwartz' theorem;
  • nonparametric mixtures.

• (80%) Homework: I will assign roughly 25 problems during the quarter. The bad news is that there will be no partial credit for homework, and you have to work on it alone. The good news is that if you get a problem wrong you can resubmit it until you get it right. You can turn in a maximum of 5 problems per week.
• (20%)Term paper: This will involve reading and writing about a modern research area in probability. More details and possible topics will be made available as the quarter progresses.