A tutorial on approximate Bayesian computation

This tutorial explains the foundation of approximate Bayesian computation (ABC), an approach to Bayesian inference that does not require the specification of a likelihood function, and hence that can be used to estimate posterior distributions of parameters for simulation-based models. We discuss briefly the philosophy of Bayesian inference and then present several algorithms for ABC. We then apply these algorithms in a number of examples. For most of these examples, the posterior distributions are known, and so we can compare the estimated posteriors derived from ABC to the true posteriors and verify that the algorithms recover the true posteriors accurately. We also consider a popular simulation-based model of recognition memory (REM) for which the true posteriors are unknown. We conclude with a number of recommendations for applying ABC methods to solve real-world problems.