Approximate Bayesian Computation

Bayesian statistics provides a principled framework for performing statistical inference for an unknown parameter of a stochastic model assumed to be responsible for generating some observed data. However, standard Bayesian algorithms to sample from the posterior require that the likelihood function, the probability density of the data given the parameter represented as a function of the parameter for fixed observed data, is computationally tractable. However, there are an increasing number of models across Science and Technology where the likelihood function is difficult or impossible to compute. When simulation from the model is comparatively cheaper, a class of likelihood-free methods called approximate Bayesian computation (ABC) can be used. However, ABC introduces an approximation to the posterior. This paper gives an introduction to ABC, describes the approximation behaviour of ABC and provides advice on the successful implementation of ABC. Some current challenges facing ABC methods are also discussed