Constructing Sobol Sequences with Better Two-Dimensional Projections

Joe, Stephen; Kuo, Frances Y.

doi:10.1137/070709359

Cited by 313 publications

(236 citation statements)

References 18 publications

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“…For original values proposed by Sobol', in particular, the uniformity of several low-dimensional projections are very poor. Better direction numbers are proposed in [26,42], for example. Fig.…”

Section: Digital Netsmentioning

confidence: 99%

Randomized Quasi-Monte Carlo: An Introduction for Practitioners

L’Ecuyer

2018

Springer Proceedings in Mathematics &Amp; Statistics

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We survey basic ideas and results on randomized quasi-Monte Carlo (RQMC) methods, discuss their practical aspects, and give numerical illustrations. RQMC can improve accuracy compared with standard Monte Carlo (MC) when estimating an integral interpreted as a mathematical expectation. RQMC estimators are unbiased and their variance converges at a faster rate (under certain conditions) than MC estimators, as a function of the sample size. Variants of RQMC also work for the simulation of Markov chains, for function approximation and optimization, for solving partial differential equations, etc. In this introductory survey, we look at how RQMC point sets and sequences are constructed, how we measure their uniformity, why they can work for high-dimensional integrals, and how can they work when simulating Markov chains over a large number of steps.

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Section: Digital Netsmentioning

confidence: 99%

Randomized Quasi-Monte Carlo: An Introduction for Practitioners

L’Ecuyer

2018

Springer Proceedings in Mathematics &Amp; Statistics

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“…The Sobol sequence generator used in CSPCA was downloaded from Dr. Frances Kuo's website (Kuo, 2010). The code, freely available there, is the one presented by Joe and Kuo (2003) with some enhancements (Joe and Kuo, 2008). It can generate sequences up to 21,201 dimensions (Kuo, 2010).…”

Section: Implementation and Set-upmentioning

confidence: 99%

A new Metropolis optimisation method, the cross-section particle collision algorithm: some preliminary results

Sacco

Rios-Coelho

2016

IJNEST

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Abstract:In this work, we introduce a new Metropolis algorithm, which is an enhancement of the recent Particle Collision Algorithm (PCA), loosely inspired by the neutron interactions in a reactor. This novel method is called the CrossSection Particle Collision Algorithm (CSPCA), as it incorporates the concept of cross-section from Reactor Physics, in the sense that points in the search space and their respective fitness-function values are analogous to the neutron cross-sections which are used to express the likelihood of interaction between an incident neutron and a target nucleus. CSPCA is compared against the original PCA and two state-of-the-art metaheuristics, differential evolution and big bang-big crunch. These methods are applied to the turbine balancing problem, which is an NP-hard (i.e. non-deterministic polynomial-time hard) combinatorial optimisation problem that can be used to assess the potential of an algorithm to be applied to Fuel Management Optimisation (FMO). CSPCA performs better than its opponents, showing potential to be used not only in FMO, but also in other nuclear science and engineering optimisation problems.

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“…One way to generate quasi-randomness is by using a so-called Sobol' sequence, see e.g. Joe & Kuo (2008) for explanations. Implementations for Sobol' sequences exist in the literature, we use a C++ program available at the authors' website http://web.maths.unsw.edu.au/~fkuo/sobol/.…”

Section: Simulationsmentioning

confidence: 99%

A quasi-Gaussian approximation for the probability distribution of correlation functions

Wilking

Schneider

2013

A&A

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Context. Whenever correlation functions are used for inference about cosmological parameters in the context of a Bayesian analysis, the likelihood function of correlation functions needs to be known. Usually, it is approximated as a multivariate Gaussian, though this is not necessarily a good approximation. Aims. We show how to calculate a better approximation for the probability distribution of correlation functions of one-dimensional random fields, which we call "quasi-Gaussian". Methods. Using the exact univariate probability distribution function (PDF) as well as constraints on correlation functions previously derived, we transform the correlation functions to an unconstrained variable for which the Gaussian approximation is well justified. From this Gaussian in the transformed space, we obtain the quasi-Gaussian PDF. The two approximations for the probability distributions are compared to the "true" distribution as obtained from simulations. Additionally, we test how the new approximation performs when used as likelihood in a toy-model Bayesian analysis. Results. The quasi-Gaussian PDF agrees very well with the PDF obtained from simulations; in particular, it provides a significantly better description than a straightforward copula approach. In a simple toy-model likelihood analysis, it yields noticeably different results than the Gaussian likelihood, indicating its possible impact on cosmological parameter estimation.

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Constructing Sobol Sequences with Better Two-Dimensional Projections

Cited by 313 publications

References 18 publications

Randomized Quasi-Monte Carlo: An Introduction for Practitioners

Randomized Quasi-Monte Carlo: An Introduction for Practitioners

A new Metropolis optimisation method, the cross-section particle collision algorithm: some preliminary results

A quasi-Gaussian approximation for the probability distribution of correlation functions

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