Speaker
Description
Quasi Monte Carlo methods are very popular in uncertainty quatification because of their high convergence order compared to Monte Carlo methods. Their downside is that they sample from a uniform distribution and, therefore, they become inefficient for problems with complex and concentrated distributions. We have developed an adaptive Quasi-Monte Carlo (aQMC) quadrature which concentrates the sampling to those subdomains with a high expected error. This is achieved by a greedy subdivision algorithm which employs an error indicator based on the modulus of continuity to control the subdivison and the subsequent resampling. We demonstrate the approach Genz' test functions and the discuss the benefits and limitations of the approach. As a semi-realistic show case, we consider a simple problem from Bayesian inference of chemical kinetic models, where concentrated posteriors naturally appear due to the high nonlinearity and sensitivity of these models and typically rather uninformative priors.
