Friday 12 September 2014
Heriot-Watt University, Edinburgh. For details of how to get to Heriot-Watt University, click here.
Talks will be held in room S.01 of the Colin Maclaurin building (building 22 on this campus map).
I am going to discuss stochastic comparison methods by outlining several examples from commutative and non-commutative probability.
We explore some connections between probability approximations and stochastic orderings. We will show how certain stochastic ordering assumptions lead to natural bounds in Poisson, compound Poisson, or compound geometric approximation. Our main example will be the Poisson case, where our ordering is closely related to well-known concepts of negative dependence such as negative relation. These results extend to the compound Poisson case. For compound geometric approximation, our stochastic ordering can be verified by finding a lower bound on a failure rate.
Based on joint work with Oliver Johnson, Claude Lefèvre and Sergey Utev.
We propose a canonical definition of the Stein operator of a univariate distribution through a skew-adjoint relationship for a differential operator or a difference operator. The resulting Stein identity not only comprises the known examples but also highlights the unifying theme as well as the flexibility in specifying the Stein identity. The identity naturally links in with a coupling approach, which we detail for sums of independent random variables. We apply our approach to the comparison of several pairs of distributions : normal vs normal, normal vs Student, maximum of random variables vs Gumbel and exponential, and beta-binomial vs Beta. The approach is applied to assess the effect of the prior distribution on the posterior distribution in Bayesian analysis.
This is joint work with Christophe Ley and Yvik Swan.
Attendance at the talks is free and there is no need to register. If you have any questions, please contact Fraser Daly.
The meeting is organized by Fraser Daly. Sponsorship from the LMS is gratefully acknowledged.