Stein’s Poisson equation was developed to enable one to bound the error in approximating the distribution of the sum of Bernoulli random variables by a Poisson distribution. In this talk we explain how Stein’s equation is derived and then show how it can be utilized in simulation. In particular we present evidence that our approach based on the Stein equation results in simulation estimators with extremely small variances when compared with other approaches. We will indicate this both analytically and empirically. We will discuss applications to such problems as determining the number of times that successive partial sums of random variables fall outside of defined limits; analyzing generalized birthday and coupon collecting problems; determining the probability that a reliability system functions, and determining the distribution of the time until a pattern appears in Markov chain generated data

### About Maths Colloquium

The Mathematics Colloquium is directed at students and academics working in the fields of pure and applied mathematics, and statistics.

We aim to present expository lectures that appeal to our wide audience.

Information for speakers

#### Information for speakers

Maths colloquia are usually held on Mondays, from 2pm to 3pm, in various locations at St Lucia.

Presentations are 50 minutes, plus five minutes for questions and discussion.

Available facilities include:

- computer
- data projector
- chalkboard or whiteboard

To avoid technical difficulties on the day, please contact us in advance of your presentation to discuss your requirements.