Nested sampling for general Bayesian computation

Skilling, John

doi:10.1214/06-ba127

Cited by 1,471 publications

(1,607 citation statements)

References 13 publications

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“…It is at least of the same complexity as a one-dimensional slice sampler, which produces an uniformly ergodic Markov chain when the likelihood L is bounded but may be slow to converge in other settings (Roberts & Rosenthal, 1999). Skilling (2006) proposes to sample values of θ by iterating M Markov chain Monte Carlo steps, using the truncated prior as the invariant distribution, and a point chosen at random among the N − 1 survivors as the starting point. Since the starting value is already distributed from the invariant distribution, a finite number M of iterations produces an outcome that is marginally distributed from the correct distribution.…”

Section: ·1 Simulating From a Constrained Priormentioning

confidence: 99%

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mentioning

confidence: 93%

“…Nested sampling was introduced by Skilling (2006) as a numerical approximation method for integrals of the kind…”

Section: Introductionmentioning

confidence: 99%

“…Skilling (2006) proposes two approaches: first, a deterministic scheme, where x i is substituted with exp(−i/N ) in (2), so that log x i is the expectation of log ϕ −1 (ϕ i ); second, a random scheme, where K parallel streams of random numbers x i,k , k = 1, . .…”

Section: Introductionmentioning

confidence: 99%

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Properties of nested sampling

Chopin¹,

Robert²

2010

Biometrika

107

129

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SUMMARYNested sampling is a simulation method for approximating marginal likelihoods proposed by Skilling (2006). We establish that nested sampling has an approximation error that vanishes at the standard Monte Carlo rate and that this error is asymptotically Gaussian. We show that the asymptotic variance of the nested sampling approximation typically grows linearly with the dimension of the parameter. We discuss the applicability and efficiency of nested sampling in realistic problems, and we compare it with two current methods for computing marginal likelihood. We propose an extension that avoids resorting to Markov chain Monte Carlo to obtain the simulated points.

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Section: ·1 Simulating From a Constrained Priormentioning

confidence: 99%

“…

…”

mentioning

confidence: 93%

“…Nested sampling was introduced by Skilling (2006) as a numerical approximation method for integrals of the kind…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Properties of nested sampling

Chopin¹,

Robert²

2010

Biometrika

107

129

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show abstract

“…Using two classes of stochastic sampling techniques, Markov-Chain Monte Carlo [20][21][22] and nested sampling [23][24][25], LALINFERENCE coherently analyzes the data from all the interferometers in the network and generates the multidimensional PDF on the full set of parameters needed to describe a binary system before marginalizing over all parameters other than the sky location (a binary in circular orbit is described by 9 to 15 parameters, depending on whether spins of the binary components are included in the model). (ii) A much faster low-latency technique, that we will call TIMING++ [8], uses data products from the search stage of the analysis, and can construct sky maps on (sub)minute time scales by using primarily time-delay information between different detector sites.…”

Section: Introductionmentioning

confidence: 99%

Reconstructing the sky location of gravitational-wave detected compact binary systems: Methodology for testing and comparison

et al. 2014

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The problem of reconstructing the sky position of compact binary coalescences detected via gravitational waves is a central one for future observations with the ground-based network of gravitational-wave laser interferometers, such as Advanced LIGO and Advanced Virgo. Different techniques for sky localization have been independently developed. They can be divided in two broad categories: fully coherent Bayesian techniques, which are high latency and aimed at in-depth studies of all the parameters of a source, including sky position, and "triangulation-based" techniques, which exploit the data products from the search stage of the analysis to provide an almost real-time approximation of the posterior probability density function of the sky location of a detection candidate. These techniques have previously been applied to data collected during the last science runs of gravitational-wave detectors operating in the so-called initial configuration. Here, we develop and analyze methods for assessing the self consistency of parameter estimation methods and carrying out fair comparisons between different algorithms, addressing issues of efficiency and optimality. These methods are general, and can be applied to parameter estimation problems other than sky localization. We apply these methods to two existing sky localization techniques representing the two above-mentioned categories, using a set of simulated inspiralonly signals from compact binary systems with a total mass of ≤ 20M ⊙ and nonspinning components. We compare the relative advantages and costs of the two techniques and show that sky location uncertainties are on average a factor ≈20 smaller for fully coherent techniques than for the specific variant of the triangulation-based technique used during the last science runs, at the expense of a factor ≈1000 longer processing time.

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Nested sampling algorithm for subsurface flow model selection, uncertainty quantification, and nonlinear calibration

2013

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[1] Calibration of subsurface flow models is an essential step for managing ground water aquifers, designing of contaminant remediation plans, and maximizing recovery from hydrocarbon reservoirs. We investigate an efficient sampling algorithm known as nested sampling (NS), which can simultaneously sample the posterior distribution for uncertainty quantification, and estimate the Bayesian evidence for model selection. Model selection statistics, such as the Bayesian evidence, are needed to choose or assign different weights to different models of different levels of complexities. In this work, we report the first successful application of nested sampling for calibration of several nonlinear subsurface flow problems. The estimated Bayesian evidence by the NS algorithm is used to weight different parameterizations of the subsurface flow models (prior model selection). The results of the numerical evaluation implicitly enforced Occam's razor where simpler models with fewer number of parameters are favored over complex models. The proper level of model complexity was automatically determined based on the information content of the calibration data and the data mismatch of the calibrated model.

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Nested sampling for general Bayesian computation

Cited by 1,471 publications

References 13 publications

Properties of nested sampling

Properties of nested sampling

Reconstructing the sky location of gravitational-wave detected compact binary systems: Methodology for testing and comparison

Nested sampling algorithm for subsurface flow model selection, uncertainty quantification, and nonlinear calibration

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