Approximate Bayesian Computation (ABC) in practice.

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 obtainable. Approximate Bayesian computation (ABC) ...

Introduction to Approximate Bayesian Computation (ABC)

M ay 2 01 1 ASYMPTOTIC BEHAVIOUR OF APPROXIMATE BAYESIAN

Although approximate Bayesian computation (ABC) has become a popular technique for performing parameter estimation when the likelihood functions are analytically intractable there has not as yet been a complete investigation of the theoretical properties of the resulting estimators. In this paper we give a theoretical analysis of the asymptotic properties of ABC based parameter estimators for h...

Approximate Bayesian computation and Bayes linear analysis: Towards high-dimensional ABC

Bayes linear analysis and approximate Bayesian computation (ABC) are techniques commonly used in the Bayesian analysis of complex models. In this article we connect these ideas by demonstrating that regression-adjustment ABC algorithms produce samples for which first and second order moment summaries approximate adjusted expectation and variance for a Bayes linear analysis. This gives regressio...

Bayesian Model Choice using Coupled ABC

In Neal (2010), a novel Approximate Bayesian Computation (ABC) algorithm, coupled ABC, was introduced. This paper shows how coupled ABC can be used in an efficient manner for model choice in a Bayesian framework. The methodology is applied to Gibbs random fields and stochastic epidemic models. Furthermore a very efficient simulation procedure for Gibbs random fields with a given sufficient summ...