politiques gouvernementales

Lemieux, Vincent

doi:10.1522/030153915

Cited by 20 publications

(36 citation statements)

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“…Unlike the MC method where confidence intervals of the estimations can be constructed using the central limit theorem, Quasi Monte Carlo methods are deterministic and they do not provide the error of the estimations. However, through the Koksma-Hlawka theorem (Lemieux 2009), an upper bound of the error of estimation by Quasi Monte Carlo methods can be assessed. In practice, this upper bound is difficult to calculate and overestimates the error.…”

Section: Array Quasi Monte Carlo Methodsmentioning

confidence: 99%

“…These methods sub-stitute random uniform variables on [0, 1] d , d ≥ 1 by deterministic sequences which have better uniformity properties. The uniformity of a sequence is measured by the so-called discrepancy (Lemieux (2009)). Sequences which have such good properties of uniformity are called Low Discrepancy Sequences (LDS).…”

Section: Introductionmentioning

confidence: 99%

“…Sequences which have such good properties of uniformity are called Low Discrepancy Sequences (LDS). There are two families of LDS (Lemieux (2009)): lattices and digital nets/sequences. Two different QMC methods are proposed for the assessment of the NPV.…”

Section: Introductionmentioning

confidence: 99%

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An application of quasi Monte Carlo methods for the numerical assessment of maintenance strategies

Demgne¹,

Lair²,

Lonchampt³

et al. 2015

Safety and Reliability of Complex Engineered Systems

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International audienceTo improve the management of maintenance planning and spare parts ordering of a fleet of components, different investments plans need to be compared. A new investments plan is compared with a reference one through an economic variable called the Net Present Value (NPV). Classically, Monte Carlo simulations are used to assess economic indicators such as the expected NPV and the probability for the NPV to be negative which stands for the probability to regret the performed investments plan. In this document, we propose to use quasi Monte Carlo methods as an alternative to the Monte Carlo (MC) method, which replace the random uniform numbers of the MC method by deterministic sequences with better uniformity properties

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Section: Array Quasi Monte Carlo Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An application of quasi Monte Carlo methods for the numerical assessment of maintenance strategies

Demgne¹,

Lair²,

Lonchampt³

et al. 2015

Safety and Reliability of Complex Engineered Systems

View full text Add to dashboard Cite

show abstract

“…Monte Carlo provides a way to average data at probabilistic intervals over time rather than through discrete time units. Equally, in cases where a large number of variables are difficult to include in mainstream quantitative models, Monte Carlo provides a means to randomly sample from or randomly generate variables of probable interest over time (Bar-Yam, 1997;Lemieux, 2009;Liang, Liu, & Carroll, 2010).…”

Section: Probability Analysismentioning

confidence: 99%

“…However, it is important to note that Monte Carlo methods provide a bridge between stochastics and Markov Chains, which will be discussed in the following section. We are able to integrate these methods into largescale projects in education, from looking globally at education financing (Lemieux, 2009) to understanding large numbers of frequency distributions in an iterative fashion (Liang, Liu, & Carroll, 2010). Mortgage backed securities, which take 20 to 30 years to mature, are difficult to project with loglinear models because this long time span opens the model up to multiple emergent anomalies.…”

Section: Probability Analysismentioning

confidence: 99%

Quantitative Research Methods in Chaos and Complexity: From Probability to Post Hoc Regression Analyses

Gilstrap¹

2013

COMPLICITY

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In addition to qualitative methods presented in chaos and complexity theories in educational research, this article addresses quantitative methods that may show potential for future research studies. Although much in the social and behavioral sciences literature has focused on computer simulations, this article explores current chaos and complexity methods that have the potential to bridge the divide between qualitative and quantitative, as well as theoretical and applied, human research studies. These methods include multiple linear regression, nonlinear regression, stochastics, Monte Carlo methods, Markov Chains, and Lyapunov exponents. A postulate for post hoc regression analysis is then presented as an example of an emergent, recursive, and iterative quantitative method when dealing with interaction effects and collinearity among variables. This postulate also highlights the power of both qualitative and quantitative chaos and complexity theories in order to observe and describe both the micro and macro levels of systemic emergence.

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Projection‐based techniques for high‐dimensional optimal transport problems

Zhang

Zhong

et al. 2022

WIREs Computational Stats

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Optimal transport (OT) methods seek a transformation map (or plan) between two probability measures, such that the transformation has the minimum transportation cost. Such a minimum transport cost, with a certain power transform, is called the Wasserstein distance. Recently, OT methods have drawn great attention in statistics, machine learning, and computer science, especially in deep generative neural networks. Despite its broad applications, the estimation of high-dimensional Wasserstein distances is a well-known challenging problem owing to the curse-of-dimensionality. There are some cutting-edge projection-based techniques that tackle high-dimensional OT problems. Three major approaches of such techniques are introduced, respectively, the slicing approach, the iterative projection approach, and the projection robust OT approach. Open challenges are discussed at the end of the review.This article is categorized under: Statistical and Graphical Methods of Data Analysis > Dimension Reduction Statistical Learning and Exploratory Methods of the Data Sciences > Manifold Learning

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politiques gouvernementales

Cited by 20 publications

References 0 publications

An application of quasi Monte Carlo methods for the numerical assessment of maintenance strategies

An application of quasi Monte Carlo methods for the numerical assessment of maintenance strategies

Quantitative Research Methods in Chaos and Complexity: From Probability to Post Hoc Regression Analyses

Projection‐based techniques for high‐dimensional optimal transport problems

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