## Elves to the ABC rescue!

Marko Järvenpää, Michael Gutmann, Arijus Pleska, Aki Vehtari, and Pekka Marttinen have written a paper on Efficient Acquisition Rules for Model-Based Approximate Bayesian Computation soon to appear in Bayesian Analysis that gives me the right nudge to mention the ELFI software they have been contributing to for a while. Where the acronym stands for engine for likelihood-free inference. Written in Python, DAG based, and covering methods like the

• ABC rejection sampler
• Sequential Monte Carlo ABC sampler
• Bayesian Optimization for Likelihood-Free Inference (BOLFI) framework
• Bayesian Optimization (not likelihood-free)
• No-U-Turn-Sampler (not likelihood-free)

[Warning: I did not experiment with the software! Feel free to share.]

“…little work has focused on trying to quantify the amount of uncertainty in the estimator of the ABC posterior density under the chosen modelling assumptions. This uncertainty is due to a finite computational budget to perform the inference and could be thus also called as computational uncertainty.”

The paper is about looking at the “real” ABC distribution, that is, the one resulting from a realistic perspective of a finite number of simulations and acceptances. By acquisition, the authors mean an efficient way to propose the next value of the parameter θ, towards minimising the uncertainty in the ABC density estimate. Note that this involves a loss function that must be chosen by the analyst and then available for the minimisation program. If this sounds complicated…

“…our interest is to design the evaluations to minimise the uncertainty in a quantity that itself describes the uncertainty of the parameters of a costly simulation model.”

it indeed is and it requires modelling choices. As in Guttman and Corander (2016), which was also concerned by designing the location of the learning parameters, the modelling is based here on a Gaussian process for the discrepancy between the observed and the simulated data. Which provides an estimate of the likelihood, later used for selecting the next sampling value of θ. The final ABC sample is however produced by a GP estimation of the ABC distribution.As noted by the authors, the method may prove quite time consuming: for instance, one involved model required one minute of computation time for selecting the next evaluation location. (I had a bit of a difficulty when reading the paper as I kept hitting notions that are local to the paper but not immediately or precisely defined. As “adequation function” [p.11] or “discrepancy”. Maybe correlated with short nights while staying at CIRM for the Masterclass, always waking up around 4am for unknown reasons!)

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