Adaptive Approximate Bayesian Computation Tolerance Selection

Umberto Simola, Jessi Cisewski-Kehe, Michael U. Gutmann, Jukka Corander

Research output: Contribution to journalArticlepeer-review


Approximate Bayesian Computation (ABC) methods are increasingly used for inference in situations in which the likelihood function is either computationally costly or intractable to evaluate. Extensions of the basic ABC rejection algorithm have improved the computational efficiency of the procedure and broadened its applicability. The ABC – Population Monte Carlo (ABC-PMC) approach has become a popular choice for approximate sampling from the posterior. ABC-PMC is a sequential sampler with an iteratively decreasing value of the tolerance, which specifies how close the simulated data need to be to the real data for acceptance. We propose a method for adaptively selecting a sequence of tolerances that improves the computational efficiency of the algorithm over other commontechniques. In addition we define a stopping rule as a by-product of the adaptationprocedure, which assists in automating termination of sampling. The proposed au-tomatic ABC-PMC algorithm can be easily implemented and we present severalexamples demonstrating its benefits in terms of computational efficiency.
Original languageEnglish
Pages (from-to)397-423
Number of pages27
JournalBayesian analysis
Issue number2
Early online date7 May 2020
Publication statusPublished - 1 Jun 2021


  • complex stochastic modeling
  • likelihood-free methods
  • sequential Monte Carlo

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