# Robust Bayesian synthetic likelihood via a semi-parametric approach

@article{An2020RobustBS, title={Robust Bayesian synthetic likelihood via a semi-parametric approach}, author={Ziwen An and David J. Nott and Christopher C. Drovandi}, journal={Statistics and Computing}, year={2020}, volume={30}, pages={543-557} }

Bayesian synthetic likelihood (BSL) is now a well-established method for performing approximate Bayesian parameter estimation for simulation-based models that do not possess a tractable likelihood function. BSL approximates an intractable likelihood function of a carefully chosen summary statistic at a parameter value with a multivariate normal distribution. The mean and covariance matrix of this normal distribution are estimated from independent simulations of the model. Due to the parametric…

## 31 Citations

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.

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.

2 Bayesian Synthetic Likelihood and Compatibility 2 . 1 Bayesian Synthetic Likelihood Framework

- Computer Science
- 2019

To circumvent the issue of incompatibility between the observed and simulated summary statistics, two robust versions of BSL are proposed that can deliver reliable performance regardless of whether or not the assumed DGP can generate simulatedsummary statistics that mimic the behavior of the observed summaries.

Robust Approximate Bayesian Inference With Synthetic Likelihood

- Computer ScienceJ. Comput. Graph. Stat.
- 2021

This work proposes a new BSL approach that can detect the presence of model misspecification, and simultaneously deliver useful inferences even under significant model missespecified, and demonstrates its superior accuracy over standard BSL when the assumed model is misspecified.

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.

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.

Approximate Bayesian inference from noisy likelihoods with Gaussian process emulated MCMC

- Computer Science
- 2021

The main methodological innovation is to model the log-likelihood function using a Gaussian process in a local fashion and apply this model to emulate the progression that an exact Metropolis-Hastings algorithm would take if it was applicable.

Parallel Gaussian Process Surrogate Bayesian Inference with Noisy Likelihood Evaluations

- Computer ScienceBayesian Analysis
- 2019

This work frames the inference task as a sequential Bayesian experimental design problem, where the log-likelihood function is modelled with a hierarchical Gaussian process (GP) surrogate model, which is used to efficiently select additional log- likelihood evaluation locations.

Score Matched Conditional Exponential Families for Likelihood-Free Inference∗

- Computer Science
- 2020

This work generates parameter-simulation pairs from the model independently on the observation, and uses them to learn a conditional exponential family likelihood approximation, which can be used as summaries in ABC, and applies this method to a challenging model from meteorology.

Sequentially Guided MCMC Proposals for Synthetic Likelihoods and Correlated Synthetic Likelihoods

- Computer ScienceBayesian Analysis
- 2022

This work introduces an algorithm producing a proposal distribution that is sequentially tuned and made conditional to data, thus it rapidly guides the proposed parameters towards high posterior density regions, and exploits strategies borrowed from the correlated pseudo-marginal MCMC literature to improve the chains mixing in a SL framework.

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