Imprecise Monte Carlo simulation and iterative importance sampling for the estimation of lower previsions

Troffaes, Matthias C. M.

doi:10.1016/j.ijar.2018.06.009

Cited by 26 publications

(25 citation statements)

References 10 publications

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“…Peng et al (2018)) developed a nonparametric uncertainty representation method with different insufficient data from two sources. Troffaes (2018)) further proposed an imprecise MC simulation and iterative importance sampling for the estimation of lower previsions. Fetz (2019)) improved the convergence of iterative importance sampling for computing upper and lower expectations.…”

Section: Modern MC Methods For Uqmentioning

confidence: 99%

Modern Monte Carlo methods for efficient uncertainty quantification and propagation: A survey

Zhang

2020

WIREs Computational Stats

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Uncertainty quantification (UQ) includes the characterization, integration, and propagation of uncertainties that result from stochastic variations and a lack of knowledge or data in the natural world. Monte Carlo (MC) method is a sampling‐based approach that has widely used for quantification and propagation of uncertainties. However, the standard MC method is often time‐consuming if the simulation‐based model is computationally intensive. This article gives an overview of modern MC methods to address the existing challenges of the standard MC in the context of UQ. Specifically, multilevel Monte Carlo (MLMC) extending the concept of control variates achieves a significant reduction of the computational cost by performing most evaluations with low accuracy and corresponding low cost, and relatively few evaluations at high accuracy and corresponding high cost. Multifidelity Monte Carlo (MFMC) accelerates the convergence of standard Monte Carlo by generalizing the control variates with different models having varying fidelities and varying computational costs. Multimodel Monte Carlo method (MMMC), having a different setting of MLMC and MFMC, aims to address the issue of UQ and propagation when data for characterizing probability distributions are limited. Multimodel inference combined with importance sampling is proposed for quantifying and efficiently propagating the uncertainties resulting from small data sets. All of these three modern MC methods achieve a significant improvement of computational efficiency for probabilistic UQ, particularly uncertainty propagation. An algorithm summary and the corresponding code implementation are provided for each of the modern MC methods. The extension and application of these methods are discussed in detail. This article is categorized under: Statistical and Graphical Methods of Data Analysis > Monte Carlo Methods Statistical and Graphical Methods of Data Analysis > Sampling

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Section: Modern MC Methods For Uqmentioning

confidence: 99%

Modern Monte Carlo methods for efficient uncertainty quantification and propagation: A survey

Zhang

2020

WIREs Computational Stats

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“…13 is now being performed on a continuous function, even if the performance function used is not smooth, or if a set of performance functions are being analysed. [30] shows that importance sampling results in a consistent estimator when the failure probability is continuous in the epistemic uncertain parameters.…”

Section: Approach 3: Metamodels For Non-naïve Approachmentioning

confidence: 98%

Robust propagation of probability boxes by interval predictor models

2020

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This paper proposes numerical strategies to robustly and efficiently propagate probability boxes through expensive black box models. An interval is obtained for the system failure probability, with a confidence level. The three proposed algorithms are sampling based, and so can be easily parallelised, and make no assumptions about the functional form of the model. In the first two algorithms, the performance function is modelled as a function with unknown noise structure in the aleatory space and supplemented by a modified performance function. In the third algorithm, an Interval Predictor Model is constructed and a re-weighting strategy used to find bounds on the probability of failure. Numerical examples are presented to show the applicability of the approach. The proposed method is flexible and can account for epistemic uncertainty contained inside the limit state function. This is a feature which, to the best of the authors' knowledge, no existing methods of this type can deal with.

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“…All the variables are assumed to be independent with respect to each other and the probability distributions associated with each of them are listed in Table 1. The mean values of a and t, are modeled as interval variables, i.e., θ 1 = µ a ∈ [11,13] and θ 2 = µ t ∈ [13,15], respectively. Note that the distributions of those parameters that must be positive due to physical reasons, i.e., a, t, b and h, are truncated such that no samples with negative values are generated.…”

Section: Examplementioning

confidence: 99%

“…For instance, series expansion methods have been introduced (see e.g., [9], [10]) to approximate the epistemic uncertain parameters via series expansion or orthogonal polynomial expansion schemes (see e.g., [11]), or Chebyshev polynomial based schemes such as presented in [12]. For a more rigorous analysis of Monte Carlo methods for propagating imprecise probabilities, the reader is referred to [13,14]. However, due to assumptions on the local nature of the solution manifold around the expansion point, these methods are often limited to small-to-moderate levels of epistemic uncertainty [15].…”

Section: Introductionmentioning

confidence: 99%

Efficient imprecise reliability analysis using the Augmented Space Integral

Yuan

Faes

Liu

et al. 2021

Reliability Engineering & System Safety

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This paper presents an efficient approach to compute the bounds on the reliability of a structure subjected to uncertain parameters described by means of imprecise probabilities. These imprecise probabilities arise from epistemic uncertainty in the definition of the hyper-parameters of a set of random variables that describe aleatory uncertainty in some of the structure's properties.Typically, such calculation involves the solution of a so-called double-loop problem, where a crisp reliability problem is repeatedly solved to determine which realisation of the epistemic uncertainties yields the worst or best case with respect to structural safety. The approach in this paper aims at decoupling this double loop by virtue of the Augmented Space Integral. The core idea of the method is to infer a functional relationship between the epistemically uncertain hyper-parameters and the probability of failure. Then, this functional relationship can be used to determine the best and worst case behaviour with respect to the probability of failure. Three case studies are included to illustrate the effectiveness and efficiency of the developed methods.

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Imprecise Monte Carlo simulation and iterative importance sampling for the estimation of lower previsions

Cited by 26 publications

References 10 publications

Modern Monte Carlo methods for efficient uncertainty quantification and propagation: A survey

Modern Monte Carlo methods for efficient uncertainty quantification and propagation: A survey

Robust propagation of probability boxes by interval predictor models

Efficient imprecise reliability analysis using the Augmented Space Integral

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