COLLOQUIUM MATHEMATICS, Prof. dr. A. van der Vaart (Leiden University, Scientific Director)

Title:

Bayesian uncertainty quantification

Abstract:

The Bayesian method in statistics consists of updating a prior probability

distribution over the set of parameters of interest to a conditional distribution

given the observed data. After reviewing how this works in the case of

a finite-dimensional parameter (as considered by Bayes, 1763), we give

some examples of the Bayesian method applied to infinite-dimensional

parameters, when prior and posterior distributions are probability distributions

over, for instance, a function space. A measure of centre of the posterior distribution

(typically the posterior mean or mode) is used as a best reconstruction of the true

parameter, while the spread in the posterior distribution should give some

indication of the remaining uncertainty of this reconstruction. We discuss

ways on how these two uses can be justified mathematically, and give some

examples of successes and failures. The talk will have a general character

and be based on insights obtained in the last 15 years.

Colloquium coordinators are Prof.dr. A.J. van der Schaft ( a.j.van.der.schaft rug.nl ),

Dr. A.V. Kiselev (e-mail: a.v.kiselev rug.nl )

http://www.rug.nl/research/jbi/news/colloquia/mathematics-colloquia/