Multicanonical Sequential Monte Carlo Sampler for Uncertainty Quantification

TL;DR

This paper introduces a parallelizable Sequential Monte Carlo sampler for multicanonical importance sampling, improving efficiency in estimating the tail distributions of system performance parameters in uncertainty quantification.

Contribution

It proposes a novel multicanonical sequential Monte Carlo method that replaces MCMC with SMC for parallel efficiency in importance sampling.

Findings

Demonstrates competitive performance with mathematical examples

Effective in reconstructing distribution tails

Suitable for parallel computing environments

Abstract

In many real-world engineering systems, the performance or reliability of the system is characterised by a scalar parameter. The distribution of this performance parameter is important in many uncertainty quantification problems, ranging from risk management to utility optimisation. In practice, this distribution usually cannot be derived analytically and has to be obtained numerically by simulations. To this end, standard Monte Carlo simulations are often used, however, they cannot efficiently reconstruct the tail of the distribution which is essential in many applications. One possible remedy is to use the Multicanonical Monte Carlo method, an adaptive importance sampling scheme. In this method, one draws samples from an importance sampling distribution in a nonstandard form in each iteration, which is usually done via Markov chain Monte Carlo (MCMC). MCMC is inherently serial and therefore struggles with parallelism. In this paper, we present a new approach, which uses the Sequential Monte Carlo sampler to draw from the importance sampling distribution, which is particularly suited for parallel implementation. With both mathematical and practical examples, we demonstrate the competitive performance of the proposed method.