Unbiased and Consistent Nested Sampling via Sequential Monte Carlo

Salomone, Robert; South, Leah F.; Drovandi, Christopher; Kroese, Dirk P.

doi:10.48550/arxiv.1805.03924

Cited by 19 publications

(39 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Recent work has proposed adapting the MCMC kernel parameters online using the population of particles. For example, Fearnhead and Taylor (2013) and Salomone et al (2018) propose adaptation methods for generic MCMC kernels. Buchholz et al (2018) propose methods for performing the notoriously challenging tuning of HMC kernel parameters in SMC.…”

Section: Sequential Monte Carlo and Control Variatesmentioning

confidence: 99%

“…This example has been considered from a Bayesian context in Girolami (2008), South et al (2018) and Salomone et al (2018). Following South et al (2018), observations y(t) of R pp (t) are observed with noise such that y(t) ∼ N (R pp (t), 0.02 2 ) for t = 0, 3, .…”

Section: Odementioning

confidence: 99%

“…The adaptive SMC methods used to select the tuning parameters and inverse temperatures are described in Salomone et al (2018) and Jasra et al (2011), respectively. The post-hoc method for adapting the inverse temperatures is described in Appendix B. where Σj is the empirical covariance and h j is a tuning parameter.…”

Section: G Implementation Detailsmentioning

confidence: 99%

“…The post-hoc method for adapting the inverse temperatures is described in Appendix B. where Σj is the empirical covariance and h j is a tuning parameter. We specify a set of 20 values which are log-uniform on the range of h min to h max and, following Salomone et al (2018), we select the value which maximises the highest median estimated expected square jumping distance (ESJD, Pasarica and Gelman (2010)). Finally, we choose the number of MCMC repeats so that a given percentage of particles have a total absolute jumping distance greater than the mean Mahalanobis distance between particles before resampling (Salomone et al, 2018).…”

Section: G Implementation Detailsmentioning

confidence: 99%

See 3 more Smart Citations

Regularised Zero-Variance Control Variates for High-Dimensional Variance Reduction

South¹,

Oates²,

Mira³

et al. 2018

Preprint

Self Cite

View full text Add to dashboard Cite

Zero-variance control variates (ZV-CV) are a post-processing method to reduce the variance of Monte Carlo estimators of expectations using the derivatives of the log target. Once the derivatives are available, the only additional computational effort is solving a linear regression problem. Significant variance reductions have been achieved with this method in low dimensional examples, but the number of covariates in the regression rapidly increases with the dimension of the target. We propose to exploit penalised regression to make the method more flexible and feasible, particularly in higher dimensions. Connections between this penalised ZV-CV approach and control functionals are made, providing additional motivation for our approach. Another type of regularisation based on using subsets of derivatives, or a priori regularisation as we refer to it in this paper, is also proposed to reduce computational and storage requirements. Methods for applying ZV-CV and regularised ZV-CV to sequential Monte Carlo (SMC) are described and a new estimator for the normalising constant of the posterior is developed to aid Bayesian model choice. Several examples showing the utility and limitations of regularised ZV-CV for Bayesian inference are given. The methods proposed in this paper are accessible through the R package ZVCV available at https://github.com/LeahPrice/ZVCV.

show abstract

Section: Sequential Monte Carlo and Control Variatesmentioning

confidence: 99%

Section: Odementioning

confidence: 99%

Section: G Implementation Detailsmentioning

confidence: 99%

Section: G Implementation Detailsmentioning

confidence: 99%

See 2 more Smart Citations

Regularised Zero-Variance Control Variates for High-Dimensional Variance Reduction

South¹,

Oates²,

Mira³

et al. 2018

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…,Salomone et al (2018) andBon et al (2021) for examples of this idea outside of the exact-approximate context. The conditional ESJD is defined as…”

mentioning

confidence: 99%

Adaptive exact-approximate sequential Monte Carlo

Botha¹,

Kohn²,

South³

et al. 2022

Preprint

View full text Add to dashboard Cite

Exact-approximate sequential Monte Carlo (SMC) methods target the exact posterior of intractable likelihood models by using a non-negative unbiased estimator of the likelihood when the likelihood is computationally intractable. For state-space models, a particle filter estimator can be used to obtain an unbiased estimate of the likelihood. The efficiency of exact-approximate SMC greatly depends on the variance of the likelihood estimator, and therefore on the number of state particles used within the particle filter. We introduce a novel method to adaptively select the number of state particles within exact-approximate SMC. We also utilise the expected squared jumping distance to trigger the adaptation, and modify the exchange importance sampling method of Chopin et al. (2012) to replace the current set of state particles with the new set. The resulting algorithm is fully adaptive, and can significantly improve current methods. Code for our methods is available at https://github.com/imkebotha/adaptive-exactapproximate-smc.

show abstract

Efficient Bayesian estimation for GARCH-type models via Sequential Monte Carlo

Clements

Drovandi

2020

Econometrics and Statistics

View full text Add to dashboard Cite

This paper exploits the advantages of sequential Monte Carlo (SMC) to develop parameter estimation and model selection methods for GARCH (Generalized Au-toRegressive Conditional Heteroskedasticity) style models. This approach provides an alternative method for quantifying estimation uncertainty relative to classical inference. We demonstrate that even with long time series, the posterior distribution of model parameters are non-normal, highlighting the need for a Bayesian approach and an efficient posterior sampling method. Efficient approaches for both constructing the sequence of distributions in SMC, and leave-one-out cross-validation, for long time series data are also proposed. Finally, we develop an unbiased estimator of the likelihood for the Bad Environment-Good Environment model, a complex GARCH-type model, which permits exact Bayesian inference not previously available in the literature.

show abstract

Unbiased and Consistent Nested Sampling via Sequential Monte Carlo

Cited by 19 publications

References 34 publications

Regularised Zero-Variance Control Variates for High-Dimensional Variance Reduction

Regularised Zero-Variance Control Variates for High-Dimensional Variance Reduction

Adaptive exact-approximate sequential Monte Carlo

Efficient Bayesian estimation for GARCH-type models via Sequential Monte Carlo

Contact Info

Product

Resources

About