Approximate Bayesian computation with differential evolution

Abstract

Approximate Bayesian computation (ABC) is a simulation-based method for estimating the posterior distribution of the parameters of a model. The ABC approach is instrumental when a likelihood function for a model cannot be mathematically specified, or has a complicated form. Although difficulty in calculating a model’s likelihood is extremely common, current ABC methods suffer from two problems that have largely prevented their mainstream adoption: long computation time and an inability to scale beyond a few parameters. We introduce differential evolution as a computationally efficient genetic algorithm for proposal generation in our ABC sampler. We show how using this method allows our new ABC algorithm, called ABCDE, to obtain accurate posterior estimates in fewer iterations than kernel-based ABC algorithms and to scale to high-dimensional parameter spaces that have proven difficult for current ABC methods.