Fundamentals and Recent Developments in Approximate Bayesian Computation

Bayesian inference plays an important role in phylogenetics, evolutionary biology and in many other branches of science. It provides a principled framework for dealing with uncertainty and quantifying how it changes in the light of new evidence. For many complex models and inference problems, however, only approximate quantitative answers are obtain algorithms for approximate inference that make a minimal set of assumptions by only requiring that sampling from a model is possible. We explain here the fundamentals of approximate Bayesian computation, review the classical algorithms, and highlight recent developments.