The calculation of precise probabilities in statistics, computer science, physics and biology under realistic model assumptions and sample sizes is often impractical, and approximation is typically required. Having a bound on the error of commonly used approximations is therefore necessary in many real applications. Stein’s method has proved itself to be a powerful tool in such situations.

Stein's method is one of the most powerful tools for proving limit theorems with sharp, explicit errors for complex dependent problems. It is curiously hard to grasp how and why it works since it avoids both characteristic functions and higher moments. The course will cover the fundamentals of Stein’s method, starting with the Normal and Poisson distributions to illustrate the construction of the Stein equation and the derivation of the properties required on its solution. A number of coupling methods for use in the Stein equation will be presented, as well as it use in cases of local dependence.

The lecture is aimed at master's students. Knowledge of analysis and basic probability theory is assumed.

Lectures: Tu 08:15-09:45, Geom H2 and Th 08:15-09:00, Geom H2 [Introductory slides]

Exercise: Th 09:00-09:45, Geom H2