ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

12. Probability and Statistics

1991 MS Classification: 60 J 15 Mathé, Peter, WIAS Berlin Efficiency of Monte Carlo Integration using Markov Chains We investigate the efficiency of numerical integration based on Markov chains. We determine how the loss of efficiency compared to independent sampling depends on spectral properties of the underlying Markov chain. This is done for discrete and non–discrete state spaces. Then we discuss how variance reduction improves efficiency. As an application we exhibit the convergence of Metropolis samplers towards their invariant distribution in dependence of the distance of this to the uniform one.