Properties of nested sampling

Chopin, Nicolás; Robert, Christian P.

doi:10.1093/biomet/asq021

Cited by 104 publications

(137 citation statements)

References 27 publications

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“…More specifically in Table 5, we maintain fixed T = 2000 whereas, in Table 6 we keep fixed the total number of generated samples N T = 2 10 5 . APIS outperforms always PMC when σ i,j ∼ U( [1,5]) and σ i,j ∼ U( [1,10]) whereas PMC provides better results for σ i,j ∼ U( [1,30]) (with the exception of the case N = 200 and T = 2000 in Table 5). This is owing to APIS, in this case with bigger variances, needs the use of a greater value of T a .…”

Section: Localization Problem In a Wireless Sensor Networkmentioning

confidence: 99%

“…Importance sampling (IS) [8,9] is a well-known MC methodology to compute efficiently integrals involving a complicated multidimensional target probability density function (pdf), π(x) with x ∈ R n . Moreover, it is often used in order to calculate the normalizing constant of π(x) (also called partition function) [9], which is required in several applications, like model selection [10,11,12].…”

Section: Introductionmentioning

confidence: 99%

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An Adaptive Population Importance Sampler: Learning From Uncertainty

Martino

Elvira

Luengo

et al. 2015

IEEE Trans. Signal Process.

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Monte Carlo (MC) methods are well-known computational techniques widely used in different fields such as signal processing, communications and machine learning. An important class of MC methods is composed of importance sampling (IS) and its adaptive extensions, e.g., Adaptive Multiple IS (AMIS) and Population Monte Carlo (PMC). In this work, we introduce a novel adaptive and iterated importance sampler using a population of proposal densities. The proposed algorithm, named Adaptive Population Importance Sampling (APIS), provides a global estimation of the variables of interest iteratively, making use of all the samples previously generated. APIS combines a sophisticated scheme to build the IS estimators (based on the deterministic mixture approach) with a simple temporal adaptation (based on epochs). In this way, APIS is able to keep all the advantages of both AMIS and PMC while minimizing their drawbacks. Futhermore, the cloud of proposals is adapted in such a way that local features of the target density can be better taken into account compared to single global adaptation procedures. The result is a fast, simple, robust and high-performance algorithm applicable to a wide range of problems. Numerical results show the advantages of the proposed sampling scheme for a toy example and a localization problem in a wireless sensor network.

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Section: Localization Problem In a Wireless Sensor Networkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An Adaptive Population Importance Sampler: Learning From Uncertainty

Martino

Elvira

Luengo

et al. 2015

IEEE Trans. Signal Process.

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“…3 The most difficult task in implementing (14) is sampling L new according to the constraint L new > L n . An approach that samples always from the whole space Θ⊕Θ M would result in an unacceptable decrease in the acceptance rate of L new with decreasing V n and increasing likelihood.…”

Section: Ellipsoidal Nested Samplingmentioning

confidence: 99%

The ellipsoidal nested sampling and the expression of the model uncertainty in measurements

Gervino

Mana

Palmisano

2016

Int. J. Mod. Phys. B

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In this paper, we consider the problems of identifying the most appropriate model for a given physical system and of assessing the model contribution to the measurement uncertainty. The above problems are studied in terms of Bayesian model selection and model averaging. As the evaluation of the "evidence" Z, i.e., the integral of Likelihood × Prior over the space of the measurand and the parameters, becomes impracticable when this space has 20 ÷ 30 dimensions, it is necessary to consider an appropriate numerical strategy. Among the many algorithms for calculating Z, we have investigated the ellipsoidal nested sampling, which is a technique based on three pillars: The study of the iso-likelihood contour lines of the integrand, a probabilistic estimate of the volume of the parameter space contained within the iso-likelihood contours and the random samplings from hyperellipsoids embedded in the integration variables. This paper lays out the essential ideas of this approach.

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“…We refer the reader to the paper by Guyader, Hengartner and Matzner-Løber [22] for details and proofs, and to Cérou, Guyader, Lelièvre and Pommier [14] for the application of this algorithm in the context of molecular dynamics. Before proceeding, let us mention that this algorithm bears a resemblance to the "Nested Sampling" approach which was proposed by Skilling in the context of sampling from general distributions and estimating their normalising constants [15,44].…”

Section: Multilevel Splitting In a Static Contextmentioning

confidence: 99%

Some Recent Results in Rare Event Estimation

Caron¹,

Guyader

Zuniga

et al. 2014

ESAIM: Proc.

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Abstract. This article presents several state-of-the-art Monte Carlo methods for simulating and estimating rare events. A rare event occurs with a very small probability, but its occurrence is important enough to justify an accurate study. Rare event simulation calls for specific techniques to speed up standard Monte Carlo sampling, which requires unacceptably large sample sizes to observe the event a sufficient number of times. Among these variance reduction methods, the most prominent ones are Importance Sampling (IS) and Multilevel Splitting, also known as Subset Simulation. This paper offers some recent results on both aspects, motivated by theoretical issues as well as by applied problems. Résumé. Cet article propose un état de l'art de plusieurs méthodes Monte Carlo pour l'estimationd'événements rares. Un événement rare est par définition un événement de probabilité très faible, mais d'importance pratique cruciale, ce qui justifie une étude précise. La méthode Monte Carlo classique s'avérant prohibitivement coûteuse, il importe d'appliquer des techniques spécifiques pour leur estimation. Celles-ci se divisent en deux grandes catégories : échantillonnage préférentiel d'un côté, méthodes multi-niveaux de l'autre. Nous présentons ici quelques résultats récents dans ces domaines, motivés par des considérations tant pratiques que théoriques.

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Properties of nested sampling

Cited by 104 publications

References 27 publications

An Adaptive Population Importance Sampler: Learning From Uncertainty

An Adaptive Population Importance Sampler: Learning From Uncertainty

The ellipsoidal nested sampling and the expression of the model uncertainty in measurements

Some Recent Results in Rare Event Estimation

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