Stat C206B/Math C223B - Stein's Method and Applications


Instructor: Nathan Ross

Office: 347 Evans

Office Hours: Immediately after class and by appt.

  Class Schedule: TuTh 5 - 6:30 in 332 Evans.

Prerequisites: Probability at the level of Stat 204 or 205A/B.

  Course Description: Stein's method is a powerful tool which was developed forty years ago to obtain error terms in distributional approximation and limit theorems. The method has found success in this program for many well known distributions in a wide variety of applications. In this course we will develop the framework of the method and apply it to numerous examples. We will also cover some more recent results which use the concepts and techniques commonly employed in Stein's method in order to obtain concentration inequalities and local limit theorems.

Topics Covered: Stein's method for approximation by the normal, Poisson, and exponential distributions, concentration inequalities, and local limit theorems.

  Texts: The material will be drawn from multiple sources, but the main texts we will use are "Normal Approximation by Stein's Method" by Chen, Goldstein, and Shao, and "Poisson Approximation" by Barbour, Holst, and Janson. Another good resource containing related material is Sourav Chatterjee's Stein's method course site from Fall 2007.
  Grading: The course grade will be determined by solutions to exercises, some lecture note write-ups, and a presentation.
  Problem Sets:
  Problem set 1 (due 4 February via email)
Problem set 2 (due 18 February via email)
Problem set 3 (due 5 March via email)
Problem set 4 (due 19 March via email)
  Solutions to the problem sets can be found on the bspace course page.
  Rough Schedule for the Course:
  1. Normal approximation (4 - 5 weeks)
    • Dependency structures
    • Exchangeable pairs
    • Size bias transform
    • Zero bias transform
  2. Poisson approximation (4 - 5 weeks)
    • Dependency structures
    • Size bias transform
    • Exchangeable pairs
  3. Exponential approximation (1 -2 weeks)
    • Equilibrium transform
    • Geometric approximation
  4. Concentration inequalities and local limit theorems (2 - 4 weeks)
    • Exchangeable pairs