ABC: a useful Bayesian tool for the analysis of population data.

Approximate Bayesian computation (ABC) is a recently developed technique for solving problems in Bayesian inference. Although typically less accurate than, for example, the frequently used Markov Chain Monte Carlo (MCMC) methods, they have greater flexibility because they do not require the specification of a likelihood function. For this reason considerable amounts of data can be analysed and more complex models can be used providing, thereby, a potential better fit of the model to the data. Since its first applications in the late 1990s its usage has been steadily increasing. The framework was originally developed to solve problems in population genetics. However, as its efficiency was recognized its popularity increased and, consequently, it started to be used in fields as diverse as phylogenetics, ecology, conservation, molecular evolution and epidemiology. While the ABC algorithm is still being greatly studied and alterations to it are being proposed, the statistical approach has already reached a level of maturity well demonstrated by the number of related computer packages that are being developed. As improved ABC algorithms are proposed, the expansion of the use of this method can only increase. In this paper we are going to depict the context that led to the development of ABC focusing on the field of infectious disease epidemiology. We are then going to describe its current usage in such field and present its most recent developments.