ABSTRACT
Approximate Bayesian computation (ABC) arose as an inferential method in population genetics to address estimation of parameters of interest such as mutation rates and demographic parameters in cases where the underlying probability models had intractable likelihoods. This chapter explains a very brief introduction to genealogical trees and the effects of mutation, focusing on the simplest case in which a panmictic population is assumed to be very large and of constant size N and within which there is no recombination. The development of ABC was predicated on the availability of computational power and the lack of tractable likelihoods. Statistical inference for the parameter θ0 for the infinitely many alleles model was the subject of Ewens' celebrated paper. Griffiths and Simon Tavare introduced another approach to full-likelihood-based inference by exploiting a classical result about Markov chains. Bayesian methods provide a natural setting for inference not just about model parameters, but also about unobservables in the underlying model.
