Modified Metropolis-Hastings algorithm with reduced chain correlation for efficient subset simulation

Abstract

Simulation of Markov chain samples using the MetropolisHastings algorithm is useful for reliability estimation. Subset simulation is an example of the reliability estimation method utilizing this algorithm. The efficiency of the simulation is governed by the correlation between the simulated Markov chain samples. The objective of this study is to propose a modified MetropolisHastings algorithm with reduced chain correlation. The modified algorithm differs from the original in terms of the transition probability. It has been verified that the modified algorithm satisfies the reversibility condition and therefore the simulated samples follow the target distribution for the correct theoretical reasons. When applied to subset simulation, the modified algorithm produces a more accurate estimate of failure probability as indicated by a lower coefficient of variation and a lower mean square error. The advantage is more significant for small failure probability. Examples of soil slope with spatially variable properties were presented to demonstrate the applicability of the proposed modification to reliability estimation of engineering problems. It was found that the modified algorithm produces a more accurate estimator over the range of random dimensions studied. © 2010 Elsevier Ltd. All rights reserved.