A benchmark study on intelligent sampling techniques in Monte Carlo simulation

Abstract

In recent years, new, intelligent and efficient sampling techniques for Monte Carlo simulation have been developed. However, when such new techniques are introduced, they are compared to one or two existing techniques, and their performance is evaluated over two or three problems. A literature survey shows that benchmark studies, comparing the performance of several techniques over several problems, are rarely found. This article presents a benchmark study, comparing Simple or Crude Monte Carlo with four modern sampling techniques: Importance Sampling Monte Carlo, Asymptotic Sampling, Enhanced Sampling and Subset Simulation; which are studied over six problems. Moreover, these techniques are combined with three schemes for generating the underlying samples: Simple Sampling, Latin Hypercube Sampling and Antithetic Variates Sampling. Hence, a total of fifteen sampling strategy combinations are explored herein. Due to space constrains, results are presented for only three of the six problems studied; conclusions, however, cover all problems studied. Results show that Importance Sampling using design points is extremely efficient for evaluating small failure probabilities; however, finding the design point can be an issue for some problems. Subset Simulation presented very good performance for all problems studied herein. Although similar, Enhanced Sampling performed better than Asymptotic Sampling for the problems considered: this is explained by the fact that in Enhanced Sampling the same set of samples is used for all support points; hence a larger number of support points can be employed without increasing the computational cost. Finally, the performance of all the above techniques was improved when combined with Latin Hypercube Sampling, in comparison to Simple or Antithetic Variates sampling.

Spatial seismic hazard variation and adaptive sampling of portfolio location uncertainty in probabilistic seismic risk analysis

“…The error convergence of different sampling schemes has been investigated for many different types of integrals and application areas (Hess et al, 2006;dos Santos and Beck, 2015). Some work has already been performed on variance reduction for probabilistic seismic hazard analysis (PSHA) and PSRA in the form of importance sampling, e.g., preferentially sampling the tails of the magnitude and site ground motion probability distributions (Jayaram and Baker, 2010;Eads et al, 2013). However, to our knowledge so far no study has specifically investigated variance reduction for location uncertainty in PSRA in a modern risk assessment framework.…”

State-of-the-art of probabilistic performance based structural fire engineering

“…The randomness in the properties could be incorporated into analyses by randomly generating fire profiles using statistical sampling methods. Some sampling methods are Monte-Carlo simulation (MCS) with Latin Hypercube sampling (LHS) method, Asymptotic Sampling, Enhanced Sampling and Subset Simulation (dos Santos and Beck, 2015;Loh, 1995).…”

Sample-based and sample-aggregated based Galerkin projection schemes for structural dynamics

“…where M k and K k−q1 correspond to the random components of M(θ) and K(θ) introduced in Equations 5and (6). The partial derivative of the random undamped eigenvectors with respect to ξ k can be expressed by a linear combination of deterministic eigenvectors.…”

“…These include principal component analysis [3], quasi Monte Carlo [4] and Latin hypercube sampling [5]. A comprehensive review of sampling techniques is given by [6]. In spite of the slow convergence rate, brute force Monte Carlo simulations are often treated as a benchmark solution in stochastic computational mechanics literature e.g.…”