Bayesian Synthetic Likelihood

By Leah Price, Christopher C. Drovandi, Anthony Lee, David J. Nott. 2017

250 citations recorded by the source corpus.

ABSTRACT Having the ability to work with complex models can be highly beneficial. However, complex models often have intractable likelihoods, so methods that involve evaluation of the likelihood function are infeasible. In these situations, the benefits of working with likelihood-free methods become apparent. Likelihood-free methods, such as parametric Bayesian indirect likelihood that uses the likelihood of an alternative parametric auxiliary model, have been explored throughout the literature as a viable alternative when the model of interest is complex. One of these methods is called the synthetic likelihood (SL), which uses a multivariate normal approximation of the distribution of a set of summary statistics. This article explores the accuracy and computational efficiency of the Bayesian version of the synthetic likelihood (BSL) approach in comparison to a competitor known as approximate Bayesian computation (ABC) and its sensitivity to its tuning parameters and assumptions. We relate BSL to pseudo-marginal methods and propose to use an alternative SL that uses an unbiased estimator of the SL, when the summary statistics have a multivariate normal distribution. Several applications of varying complexity are considered to illustrate the findings of this article. Supplemental materials are available online. Computer code for implementing the methods on all examples is available at https://github.com/cdrovandi/Bayesian-Synthetic-Likelihood.

View Paper: https://www.semanticscholar.org/paper/6b130b8f2074ec2ffd59a8183a7b20746ff9ad37

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Citations in the corpus

Likelihood-free inference with emulator networks (2018, methodology): “In synthetic likelihood approaches to ABC [10, 11, 12], one instead uses density estimation to approximate the likelihood p ( s ( x o ) | θ ) on summary statistics of simulated data.”
Flexible statistical inference for mechanistic models of neural dynamics (2017, background): “While the Gaussianity assumption is often motivated by the central limit theorem, distributions over features can in practice be complex and highly non-Gaussian [32].”
Sequential Neural Likelihood: Fast Likelihood-free Inference with Autoregressive Flows (2018, methodology): “Synthetic Likelihood [20, 57, 63, 85] estimates the mean m θ and co-variance matrix S θ of a batch of data x n ∼ p ( x | θ ) sampled at a given θ , and then approximates p ( x | ≈ Non-Gaussian likelihood approximations are also possible, e.g. saddlepoint approximations [22].”
Robust generalised Bayesian inference for intractable likelihoods (2021, unknown): “…computation and Bayesian synthetic likelihood ; Beaumont et al., 2002; Cherief-Abdellatif & Alquier, 2020; Frazier, 2020; Marin et al., 2012; Price et al., 2018; Tavaré et al., 1997), (2) auxiliary variable MCMC (such as the exchange algorithm and pseudo-marginal MCMC; Andrieu & Roberts,…”
Dynamic Likelihood-free Inference via Ratio Estimation (DIRE) (2018, methodology): “We considered the problem of learning summary statistics for likelihood-free inference by ratio estimation (LFIRE, Dutta et al. 2016), an approach that generalizes the synthetic likelihood method by Wood (2010); Price et al. (2017).”
Likelihood-Free Inference by Ratio Estimation (2016, methodology): “The results are in line with those presented by Price et al. (2017) who used synthetic likelihood, but employing a much larger number of simulations (namely n θ ∈ { 2500 , 5000 , 10000 } ).”