ABSTRACT
This chapter explains an intuitive exploration of the basics of approximate Bayesian computation (ABC) methods, and illustrates wherever possible by simple examples. It focuses on the use of simple rejection sampling-based ABC samplers. The chapter describes the exact form of the ABC approximation to the posterior distribution that is produced from the likelihood-free rejection algorithm. It compares an ABC approach to the importance sampling method that targets the true likelihood. The choice of summary statistics for an ABC analysis is a critical decision that directly affects the quality of the posterior approximation. The identification of suitable summary statistics is clearly a critical part of any analysis. The primary challenge in implementing an ABC analysis is to reduce the impact of the approximation, while restricting the required computation to acceptable levels. ABC methods are based on an inherently simple mechanism, simulating data under the model of interest and comparing the output to the observed dataset.
