Approximate Bayesian Computation: A Survey on Recent Results

Abstract

Approximate Bayesian Computation (ABC) methods have become a "mainstream" statistical technique in the past decade, following the realisation by statisticians that they are a special type of non-parametric inference. In this survey of ABC methods, we focus on the recent literature, building on the previous survey of Marin et al. Stat Comput 21(2):279-291, 2011, [39]. Given the importance of model choice in the applications of ABC, and the associated difficulties in its implementation, we also give emphasis to this aspect of ABC techniques.

Model Misspecification in Approximate Bayesian Computation: Consequences and Diagnostics

“…In a Bayesian inference paradigm, these situations have led to the rise of approximate Bayesian computation (ABC) methods that eschew calculation of the likelihood in favour of simulation; for reviews on ABC methods see, for example, Marin et al . (), Robert () and Sisson et al . ().…”

“…It is now routine in the astronomic, ecological and genetic sciences, as well as in economics and finance, that the models used to describe observed data are so complex that the likelihoods associated with these models can be computationally intractable. In a Bayesian inference paradigm, these situations have led to the rise of approximate Bayesian computation (ABC) methods that eschew calculation of the likelihood in favour of simulation; for reviews on ABC methods see, for example, Marin et al (2012), Robert (2016) and Sisson et al (2018).…”

Identification of the relative timing of infectiousness and symptom onset for outbreak control

“…This has led to methods based on approximate Bayesian computation (ABC), which requires only simulation of realisations from each model, and is computationally feasible for a wide range of models. Unfortunately, there exists 'a fundamental difficulty' in establishing robust methods based upon summary statistics ( Robert et al, 2011;Robert, 2016 ); however, see the recent work of Dehideniya et al ( Dehideniya et al, 2018 ).…”

Approximate Bayesian computation in controlled branching processes: the role of summary statistics

“…Focusing mainly on a Bayesian outlook, approximate Bayesian computation (ABC) methodology has been used widely and successfully in many fields. A detailed summary on the fundamentals of ABC methods, the classical algorithms and recent developments can be found in [18] or [25]. In particular, in the field of CBPs, the precursor paper [9] tackled the estimation of the offspring distribution of a CBP with a deterministic control function by comparing the rejection ABC algorithm with a Markov chain Monte Carlo (MCMC) method.…”