Modified metropolis-hastings algorithm with delayed rejection for high-dimensional reliability analysis

Abstract eng:
The development of an efficient MCMC strategy for sampling from complex distributions is a difficult task that needs to be solved for calculating small failure probabilities encountered in high-dimensional reliability analysis of engineering systems. Usually different variations of the Metropolis-Hastings algorithm (MH) are used. However, the standard MH algorithm does generally not work in high dimensions, since it leads to very frequent repeated samples. In order to overcome this deficiency one can use the Modified Metropolis-Hastings algorithm (MMH) proposed in [1]. Another variation of the MH algorithm, called MetropolisHastings algorithm with delayed rejection (MHDR) has been proposed by [2]. The key idea behind the MHDR algorithm is to reduce the correlation between states of the Markov chain. In this paper we combine the ideas of MMH and MHDR and propose a novel modification of the MH algorithm, called Modified Metropolis-Hastings algorithm with delayed rejection (MMHDR). The efficiency of the new algorithm is demonstrated with a numerical example where MMHDR is used together with Subset simulation for computing small failure probabilities in high dimensions.

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