Properties of nested sampling

By Nicolas Chopin, Christian P. Robert. 2008

123 citations recorded by the source corpus.

Nested sampling is a simulation method for approximating marginal likelihoods. We establish that nested sampling has an approximation error that vanishes at the standard Monte Carlo rate and that this error is asymptotically Gaussian. It is shown 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 compare it with two current methods for computing marginal likelihood. Finally, we propose an extension that avoids resorting to Markov chain Monte Carlo simulation to obtain the simulated points. Copyright 2010, Oxford University Press.

View Paper: https://www.semanticscholar.org/paper/15d89dbe8fa51ce8d415409d2a646154435752b3

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Citations in the corpus

Model selection in finite element model updating using the Bayesian evidence statistic (2011, methodology): “The updating method proposed in this paper does not place any prior assumption on the form of the posterior distribution of the model but has recently [8] been shown to perform better for normally distributed functions.”
Testing hypotheses via a mixture estimation model (2014, background): “…of marginal likelihoods is difficult in most settings (Chen et al., 2000; Marin and Robert, 2011) with further controversy about which solution to adopt (Newton and Raftery, 1994; Neal, 1994; Green, 1995; Chib, 1995; Neal, 1999; Skilling, 2006; Steele et al., 2006; Chopin and Robert, 2010).”
Estimating the evidence – a review (2011, methodology): “The algorithm may be terminated after a given number of iterations, when new contributions to ̂(y) are below some small fraction of the current value as suggested by Chopin and Robert (2010), or using one of the criteria outlined in Skilling (2006). Nested sampling is a popular algorithm in the ast”
Importance Nested Sampling and the MultiNest Algorithm (2013, background): “We agree that this is true and Chopin and Robert (2010) give a valid proof in their Appendix based on the Monotone Convergence Theorem.”
TAU-REX I: A NEXT GENERATION RETRIEVAL CODE FOR EXOPLANETARY ATMOSPHERES (2014, background): “Nested sampling (NS) algorithms (Skilling 2004, 2006; Mukherjee et al. 2006; Chopin & Robert 2010; Keeton 2011; Jasa & Xiang 2005) are becoming increasing popular in extrasolar planets (e.g. Kipping et al. 2012; Placek et al. 2013).”
Efficient Bayesian inference of subsurface flow models using nested sampling and sparse polynomial chaos surrogates (2014, methodology): “distribution has its cumulative quantity distributed according to the distribution Beta (N, 1) [37,42].”