Approximate Bayesian Computation
Posterior updates without likelihood
August 25, 2020 — September 19, 2021
Bayes
feature construction
likelihood free
machine learning
Monte Carlo
probabilistic algorithms
probability
signal processing
state space models
statistics
time series
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Approximate Bayesian Computation is a terribly underspecified description. There are many ways that inference can be based on 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
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Sisson, S. A., Fan, and Tanaka. 2007. “Sequential Monte Carlo Without Likelihoods.” Proceedings of the National Academy of Sciences.
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