Efficient Bayesian synthetic likelihood with whitening transformations

Priddle, Jacob W.; Sisson, Scott A.; Frazier, David T.; Drovandi, Christopher

doi:10.48550/arxiv.1909.04857

Cited by 3 publications

(14 citation statements)

References 25 publications

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“…For example, An et al (2020) develop a semi-parametric estimator that it is more robust to the Gaussian assumption. Further, Priddle et al (2020) consider a whitening transformation to de-correlate summary statistics combined with a shrinkage estimator of the covariance to reduce the number of model simulations required to precisely estimate the synthetic likelihood. See Drovandi et al (2018) for some other extensions to BSL.…”

Section: Likelihood-free Bayesian Inferencementioning

confidence: 99%

“…The next example we consider is the individual-based movement model of Fowler's Toads (Anaxyrus fowleri ) developed by Marchand et al (2017). The model has since been considered as a test example in likelihood-free literature, in particular for synthetic likelihood methods (see An et al 2020;Frazier and Drovandi 2021;Priddle et al 2020). We consider the "random return" model of Marchand et al (2017).…”

Section: Toad Examplementioning

confidence: 99%

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A Comparison of Likelihood-Free Methods With and Without Summary Statistics

Drovandi¹,

Frazier²

2021

Preprint

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Likelihood-free methods are useful for parameter estimation of complex models with intractable likelihood functions for which it is easy to simulate data. Such models are prevalent in many disciplines including genetics, biology, ecology and cosmology. Likelihood-free methods avoid explicit likelihood evaluation by finding parameter values of the model that generate data close to the observed data. The general consensus has been that it is most efficient to compare datasets on the basis of a low dimensional informative summary statistic, incurring information loss in favour of reduced dimensionality. More recently, researchers have explored various approaches for efficiently comparing empirical distributions in the likelihood-free context in an effort to avoid data summarisation. This article provides a review of these full data distance based approaches, and conducts the first comprehensive comparison of such methods, both qualitatively and empirically. We also conduct a substantive empirical comparison with summary statistic based likelihood-free methods. The discussion and results offer guidance to practitioners considering a likelihood-free approach. Whilst we find the best approach to be problem dependent, we also find that the full data distance based approaches are promising and warrant further development. We discuss some opportunities for future research in this space.

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Section: Likelihood-free Bayesian Inferencementioning

confidence: 99%

Section: Toad Examplementioning

confidence: 99%

A Comparison of Likelihood-Free Methods With and Without Summary Statistics

Drovandi¹,

Frazier²

2021

Preprint

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“…We now propose a method to improve the computational efficiency of semiBSL. Namely, we extend the whitening BSL (wBSL) methodology proposed by Priddle et al (2020) to the semiBSL context. The motivation behind wBSL is articulated in Theorem 1 of Priddle et al (2020).…”

Section: Whitening Semibslmentioning

confidence: 99%

“…Despite the appeal of semiBSL, the number of model simulations required to accurately estimate the correlation matrix scales poorly with the dimension of the summary statistic. The equivalent problem for sBSL, the scaling of the estimation of covariance matrix with the number of model simulations, has been explored by An et al (2019), Ong et al (2018a), Ong et al (2018b), Everitt (2017), Frazier et al (2019) and Priddle et al (2020). However, there are currently no methods designed specifically for the semi-parametric estimator, which, in practice, may preclude its application to problems where model simulation is computationally expensive.…”

Section: Introductionmentioning

confidence: 99%

“…However, there are currently no methods designed specifically for the semi-parametric estimator, which, in practice, may preclude its application to problems where model simulation is computationally expensive. The first contribution of this article adapts and extends the methodology presented in Priddle et al (2020), which combines a whitening transformation with shrinkage covariance matrix estimation, to the semiBSL context.…”

Section: Introductionmentioning

confidence: 99%

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Transformations in Semi-Parametric Bayesian Synthetic Likelihood

Priddle¹,

Drovandi²

2020

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Bayesian synthetic likelihood (BSL) is a popular method for performing approximate Bayesian inference when the likelihood function is intractable. In synthetic likelihood methods, the likelihood function is approximated parametrically via model simulations, and then standard likelihood-based techniques are used to perform inference. The Gaussian synthetic likelihood estimator has become ubiquitous in BSL literature, primarily for its simplicity and ease of implementation. However, it is often too restrictive and may lead to poor posterior approximations. Recently, a more flexible semi-parametric Bayesian synthetic likelihood (semiBSL) estimator has been introduced, which is significantly more robust to irregularly distributed summary statistics. In this work, we propose a number of extensions to semiBSL. First, we consider even more flexible estimators of the marginal distributions using transformation kernel density estimation. Second, we propose whitening semiBSL (wsemiBSL) -a method to significantly improve the computational efficiency of semiBSL. wsemiBSL uses an approximate whitening transformation to decorrelate summary statistics at each algorithm iteration. The methods developed herein significantly improve the versatility and efficiency of BSL algorithms.

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Synthetic Likelihood in Misspecified Models: Consequences and Corrections

Frazier,

Drovandi,

Nott

2021

Preprint

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We analyse the behaviour of the synthetic likelihood (SL) method when the model generating the simulated data differs from the actual data generating process. One of the most common methods to obtain SL-based inferences is via the Bayesian posterior distribution, with this method often referred to as Bayesian synthetic likelihood (BSL). We demonstrate that when the model is misspecified, the BSL posterior can be poorly behaved, placing significant posterior mass on values of the model parameters that do not represent the true features observed in the data. Theoretical results demonstrate that in misspecified models the BSL posterior can display a wide range of behaviours depending on the level of model misspecification, including being asymptotically non-Gaussian. Our results suggest that a recently proposed robust BSL approach can ameliorate this behavior and deliver reliable posterior inference under model misspecification. We document all theoretical results using a simple running example.

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Efficient Bayesian synthetic likelihood with whitening transformations

Cited by 3 publications

References 25 publications

A Comparison of Likelihood-Free Methods With and Without Summary Statistics

A Comparison of Likelihood-Free Methods With and Without Summary Statistics

Transformations in Semi-Parametric Bayesian Synthetic Likelihood

Synthetic Likelihood in Misspecified Models: Consequences and Corrections

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