Rare event probability estimation for connectivity of large random graphs

Abstract

Spatial statistical models are of considerable practical and theoretical interest. However, there has been little work on rare-event probability estimation for such models. In this paper we present a conditional Monte Carlo algorithm for the estimation of the probability that random graphs related to Bernoulli and continuum percolation are connected. Numerical results are presented showing that the conditional Monte Carlo estimators significantly outperform the crude simulation estimators.