Bayesian Synthetic Likelihood

Frazier, David T.; Drovandi, Christopher; Nott, David J.

doi:10.1002/9781118445112.stat08436

Wiley StatsRef: Statistics Reference Online 2023

DOI: 10.1002/9781118445112.stat08436

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Bayesian Synthetic Likelihood

David T. Frazier,

Christopher Drovandi,

David J. Nott

Abstract: Bayesian statistics is concerned with conducting posterior inference for the unknown quantities in a given statistical model. Conventional Bayesian inference requires the specification of a probabilistic model for the observed data, and the construction of the resulting likelihood function. However, sometimes the model is so complicated that evaluation of the likelihood is infeasible, which renders exact Bayesian inference impossible. Bayesian synthetic likelihood (BSL) is a posterior approximation procedure t… Show more

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Cited by 2 publications

References 26 publications

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A comparison of likelihood-free methods with and without summary statistics

Drovandi

Frazier

2022

Stat Comput

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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 of the data 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. Computer code to implement the methods discussed in this paper can be found at https://github.com/cdrovandi/ABC-dist-compare.

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A comparison of likelihood-free methods with and without summary statistics

Drovandi

Frazier

2022

Stat Comput

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Summary statistics and discrepancy measures for approximate Bayesian computation via surrogate posteriors

Forbes

Nguyen

et al. 2022

Stat Comput

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A key ingredient in approximate Bayesian computation (ABC) procedures is the choice of a discrepancy that describes how different the simulated and observed data are, often based on a set of summary statistics when the data cannot be compared directly. Unless discrepancies and summaries are available from experts or prior knowledge, which seldom occurs, they have to be chosen, and thus their choice can affect the quality of approximations. The choice between discrepancies is an active research topic, which has mainly considered data discrepancies requiring samples of observations or distances between summary statistics. In this work, we introduce a preliminary learning step in which surrogate posteriors are built from finite Gaussian mixtures using an inverse regression approach. These surrogate posteriors are then used in place of summary statistics and compared using metrics between distributions in place of data discrepancies. Two such metrics are investigated: a standard L2 distance and an optimal transportbased distance. The whole procedure can be seen as an extension of 1 L A T E X template 2Summary statistics and discrepancy measures for ABC via surrogate posteriors the semi-automatic ABC framework to a functional summary statistics setting and can also be used as an alternative to sample-based approaches. The resulting ABC quasi-posterior distribution is shown to converge to the true one, under standard conditions. Performance is illustrated on both synthetic and real data sets, where it is shown that our approach is particularly useful when the posterior is multimodal.

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Bayesian Synthetic Likelihood

Cited by 2 publications

References 26 publications

A comparison of likelihood-free methods with and without summary statistics

A comparison of likelihood-free methods with and without summary statistics

Summary statistics and discrepancy measures for approximate Bayesian computation via surrogate posteriors

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