Robust Approximate Bayesian Inference with Synthetic Likelihood

Frazier, David T.; Drovandi, Christopher

doi:10.48550/arxiv.1904.04551

Cited by 7 publications

(15 citation statements)

References 16 publications

(37 reference statements)

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“…For example, An et al (2019a) develop a semi-parametric synthetic likelihood, which is more robust to departures from normality. Further, Frazier and Drovandi (2019) develop synthetic likelihood methods that are more robust when there is incompatibility between the model and observed summary statistic. An alternative extension could involve a method for automatically finding a whitening transformation that minimises the loss of accuracy compared to standard BSL.…”

Section: Discussionmentioning

confidence: 99%

Efficient Bayesian synthetic likelihood with whitening transformations

Priddle¹,

Sisson²,

Frazier³

et al. 2019

Preprint

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Likelihood-free methods are an established approach for performing approximate Bayesian inference for models with intractable likelihood functions. However, they can be computationally demanding. Bayesian synthetic likelihood (BSL) is a popular such method that approximates the likelihood function of the summary statistic with a known, tractable distribution -typically Gaussian -and then performs statistical inference using standard likelihood-based techniques. However, as the number of summary statistics grows, the number of model simulations required to accurately estimate the covariance matrix for this likelihood rapidly increases. This poses significant challenge for the application of BSL, especially in cases where model simulation is expensive. In this article we propose whitening BSL (wBSL) -an efficient BSL method that uses approximate whitening transformations to decorrelate the summary statistics at each algorithm iteration. We show empirically that this can reduce the number of model simulations required to implement BSL by more than an order of magnitude, without much loss of accuracy. We explore a range of whitening procedures and demonstrate the performance of wBSL on a range of simulated and real modelling scenarios from ecology and biology.

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Section: Discussionmentioning

confidence: 99%

Efficient Bayesian synthetic likelihood with whitening transformations

Priddle¹,

Sisson²,

Frazier³

et al. 2019

Preprint

Self Cite

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“…Recently, asymptotic properties of BSL have been derived under various assumptions. Frazier and Drovandi (2019) develop a result for posterior concentration and Nott et al (2019) show that the BSL posterior mean is consistent and asymptotically normally distributed.…”

Section: ∝ P(y|θ)p(θ)mentioning

confidence: 98%

“…In a future release we plan to incorporate the methods of Frazier and Drovandi (2019), which allows BSL to be much more computationally efficient when the model is misspecified, in particular when the model is unable to recover the observed value of the summary statistic. All of the methods in our BSL package use MCMC to explore the parameter space, and can thus be slow when model simulation is computationally intensive and there is a large number of parameters.…”

Section: Selecting the Penalty Parameter For Shrinkagementioning

confidence: 99%

BSL: An R Package for Efficient Parameter Estimation for Simulation-Based Models via Bayesian Synthetic Likelihood

An¹,

South²,

Drovandi³

2019

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Bayesian synthetic likelihood (BSL) (Price et al., 2018) is a popular method for estimating the parameter posterior distribution for complex statistical models and stochastic processes that possess a computationally intractable likelihood function. Instead of evaluating the likelihood, BSL approximates the likelihood of a judiciously chosen summary statistic of the data via model simulation and density estimation. Compared to alternative methods such as approximate Bayesian computation (ABC), BSL requires little tuning and requires less model simulations than ABC when the chosen summary statistic is high-dimensional. The original synthetic likelihood relies on a multivariate normal approximation of the intractable likelihood, where the mean and covariance are estimated by simulation. An extension of BSL considers replacing the sample covariance with a penalised covariance estimator to reduce the number of required model simulations. Further, a semi-parametric approach has been developed to relax the normality assumption. In this paper, we present an R package called BSL that amalgamates the aforementioned methods and more into a single, easy-to-use and coherent piece of software. The R package also includes several examples to illustrate how to use the package and demonstrate the utility of the methods.

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“…An additional adjustment approach is considered that weights the individual summaries used in the analysis in such a way that if the simulated and observed summaries do not agree, the overall distance can still be made small. This new adjustment approach to ABC is inspired by the adjustment idea in Frazier and Drovandi (2019). In the context of Bayesian synthetic likelihood (BSL, Wood, 2010, Price et al, 2018, Frazier and Drovandi (2019) demonstrate that when the model is misspecified BSL can deliver misleading inference.…”

Section: Introductionmentioning

confidence: 99%

“…This new adjustment approach to ABC is inspired by the adjustment idea in Frazier and Drovandi (2019). In the context of Bayesian synthetic likelihood (BSL, Wood, 2010, Price et al, 2018, Frazier and Drovandi (2019) demonstrate that when the model is misspecified BSL can deliver misleading inference. To circumvent this issue, Frazier and Drovandi (2019) augment the BSL posterior with additional parameters that "soak up" the model misspecification.…”

Section: Introductionmentioning

confidence: 99%

Robust Approximate Bayesian Computation: An Adjustment Approach

Frazier,

Drovandi,

Loaiza-Maya

2020

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We propose a novel approach to approximate Bayesian computation (ABC) that seeks to cater for possible misspecification of the assumed model. This new approach can be equally applied to rejection-based ABC and to popular regression adjustment ABC. We demonstrate that this new approach mitigates the poor performance of regression adjusted ABC that can eventuate when the model is misspecified. In addition, this new adjustment approach allows us to detect which features of the observed data can not be reliably reproduced by the assumed model. A series of simulated and empirical examples illustrate this new approach.

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Robust Approximate Bayesian Inference with Synthetic Likelihood

Cited by 7 publications

References 16 publications

Efficient Bayesian synthetic likelihood with whitening transformations

Efficient Bayesian synthetic likelihood with whitening transformations

BSL: An R Package for Efficient Parameter Estimation for Simulation-Based Models via Bayesian Synthetic Likelihood

Robust Approximate Bayesian Computation: An Adjustment Approach

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