# Approximate Bayesian Computation

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?

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.

## 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.

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