# Robust Approximate Bayesian Inference With Synthetic Likelihood

@article{Frazier2021RobustAB, title={Robust Approximate Bayesian Inference With Synthetic Likelihood}, author={David T. Frazier and Christopher C. Drovandi}, journal={Journal of Computational and Graphical Statistics}, year={2021}, volume={30}, pages={958 - 976} }

Abstract Bayesian synthetic likelihood (BSL) is now an established method for conducting approximate Bayesian inference in models where, due to the intractability of the likelihood function, exact Bayesian approaches are either infeasible or computationally too demanding. Implicit in the application of BSL is the assumption that the data-generating process (DGP) can produce simulated summary statistics that capture the behaviour of the observed summary statistics. We demonstrate that if this…

## 19 Citations

Synthetic Likelihood in Misspecified Models: Consequences and Corrections

- Computer Science
- 2021

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.

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

- Computer Science, MathematicsJ. Stat. Softw.
- 2022

An R package called BSL is presented that amalgamates the aforementioned methods and more into a single, easy-to-use and coherent piece of software.

Bayesian inference using synthetic likelihood: asymptotics and adjustments

- Computer Science, MathematicsJournal of the American Statistical Association
- 2022

It is shown that Bayesian synthetic likelihood is computationally more efficient than approximate Bayesian computation, and behaves similarly to regression-adjusted approximate Bayesesian computation.

Efficient Bayesian Synthetic Likelihood With Whitening Transformations

- Computer ScienceJ. Comput. Graph. Stat.
- 2022

This article proposes whitening BSL (wBSL)—an efficient BSL method that uses approximate whitening transformations to decorrelate the summary statistics at each algorithm iteration, and shows empirically that this can reduce the number of model simulations required to implement BSL by more than an order of magnitude.

Transformations in Semi-Parametric Bayesian Synthetic Likelihood

- Computer Science
- 2020

A number of extensions to semiBSL are proposed that significantly improve the versatility and efficiency of BSL algorithms and consider even more flexible estimators of the marginal distributions using transformation kernel density estimation.

Detecting Model Misspecification in Amortized Bayesian Inference with Neural Networks

- Computer Science
- 2021

An augmented optimization objective is proposed which imposes a probabilistic structure on the learned latent data summary space and utilize maximum mean discrepancy (MMD) to detect potentially catastrophic misspeciﬁcations during inference undermining the validity of the obtained results.

Detecting conflicting summary statistics in likelihood-free inference

- Computer ScienceStat. Comput.
- 2021

Using a recent idea from the interpretable machine learning literature, some regression-based diagnostic methods are developed which are useful for detecting when different parts of a summary statistic vector contain conflicting information about the model parameters.

Robust Approximate Bayesian Computation: An Adjustment Approach

- Computer Science, Economics
- 2020

A novel approach to approximate Bayesian computation (ABC) that seeks to cater for possible misspecification of the assumed model and mitigates the poor performance of regression adjusted ABC that can eventuate when the model is misspecified.

Modularized Bayesian analyses and cutting feedback in likelihood-free inference

- Computer Science
- 2022

A semi-modular approach to likelihood-free inference where feedback is partially cut based on Gaussian mixture approximations to the joint distribution of parameters and data summary statistics is developed.

On a Variational Approximation based Empirical Likelihood ABC Method

- Computer Science
- 2020

This article shows that the target log-posterior can be approximated as a sum of an expected joint log-likelihood and the differential entropy of the data generating density, and proposes an easy-to-use empirical likelihood ABC method.

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