# Approximate Bayesian Computation

Posterior updates without likelihood

August 25, 2020 — September 20, 2021

Approximate Bayesian Computation is a terribly underspecified description. There are many ways that inference can be based upon simulations, many types of freedom from likelihood and many ways to approximate Bayesian computation. This page is about the dominant use of that term, which is the use of Simulation-based inference to do Bayes updates where the likelihood is not available but where we can simulate from the generative model.

Obviously there are other ways you can approximate Bayesian computation — see e.g. variational Bayes.

TBD: relationship between this and simulation-based inference in a frequentist setting, often called indirect inference. They look similar but tend not to cite each other. Is this a technical or sociological hurdle?

Miles Cranmer’s Introduction to Simulation-based inference.

Maybe check the reading list for ABC toolkit ELFI.

## 1 SMC for ABC

One can solve for ABC using Sequential Monte Carlo. TBD.

## 2 Bayesian Synthetic Likelihood

TBD. Something about assuming the summary statistic is close to jointly Gaussian.

## 3 Neural methods

## 4 SBC

Simulation-based Bayes calibration. Is this the same thing?

Martin Modrák, SBC Tutorial

## 5 Generalized Bayesian computation

A KL-free Bayesian computation extension. See generalized Bayes.

## 6 References

*Entropy*.

*arXiv:1907.03382 [Cs, Stat]*.

*Genetics*.

*Statistics and Computing*.

*arXiv:2102.07850 [Cs, Stat]*.

*Proceedings of the National Academy of Sciences*.

*Journal of the Royal Statistical Society: Series B (Methodological)*.

*arXiv:2103.02407 [Stat]*.

*arXiv:1803.06645 [Stat]*.

*Stat*.

*arXiv:1501.01265 [Stat]*.

*Journal of Computational and Graphical Statistics*.

*arXiv:1902.04827 [Stat]*.

*arXiv:2011.01808 [Stat]*.

*Journal of Econometrics*.

*Transactions on Machine Learning Research*.

*Journal of Computational and Graphical Statistics*.

*Proceedings of the 20th International Conference on Artificial Intelligence and Statistics (AISTATS)*. Proceedings of Machine Learning Research.

*University of California, Berkeley, Rep*.

*Symposium on Advances in Approximate Bayesian Inference*.

*Proceedings of the Thirtieth Conference on Uncertainty in Artificial Intelligence*. UAI’14.

*Statistics and Computing*.

*Statistics and Computing*.

*Computational Statistics & Data Analysis*.

*Advances in Neural Information Processing Systems 29*.

*Annals of Statistics*.

*arXiv:2103.10522 [Stat]*.

*Psychological Methods*.

*arXiv:2011.08644 [Stat]*.

*Handbook of Approximate Bayesian Computation*.

*Proceedings of the National Academy of Sciences*.

*arXiv:1808.00973 [Hep-Ph, Physics:physics, Stat]*.

*Journal of Computational and Graphical Statistics*.

*Advances in Neural Information Processing Systems 30*.

*arXiv:2110.14082 [q-Bio, Stat]*.