On March 10th, the seminar series welcomed Alexandra Gessner, a PhD student at the Max-Planck Institute in Tübingen, Germany. Alexandra introduced her work which presents a novel sampling method that enables rejection-free sampling from linearly constrained Gaussian domains. An abstract for Alexandra’s talk is given below.
Abstract
Gaussian densities are ubiquitous in statistics, yet Gaussian probabilities are notoriously hard to compute in multiple dimensions. They require integration over constrained volumes that, to further complicate matters, often encompass a very small probability mass.
I will present an adapted version of elliptical slice sampling (ESS) that enables rejection-free sampling from such linearly constrained Gaussian domains.
This version of ESS forms the basis for the integration procedure, which relies on the so-called Holmes-Diaconis-Ross (HDR) method. HDR takes a sequence of nested domains to estimate very small probability masses by sequentially computing easier conditional probabilities. Remarkably, HDR even enables the direct computation of the logarithm of the integral value.