10 Years of software development for approximate bayesian computation

Approximate Bayesian computation (ABC) is a recent developed statistical methodology that allows one to apply likelihood-free Bayesian statistics to complex models. This method relies on two main approximations: the use of Monte Carlo simulations, that avoid the need to use explicit likelihood functions; and the use of summary statistics to summarize data, which significantly reduces the amount of data to handle. The first approximation is particularly interesting in that it allows researchers to perform Bayesian inference provided they can generate simulations from the models of interest. Furthermore, one is not bound to a particular model. In fact one can assess the relative fit of different models just by evaluating the fit of the simulated data for all of them. These properties make ABC a powerful tool for statistical inference, which can be applied to many different fields. This method can be particularly attractive for computer scientists since their know-how in software development can be of great value. ABC can also be a very "democratic" method in the sense that, as long as computer packages are available, even researchers with just standard statistical knowledge can perform complex Bayesian inferences.ABC has been developed in the late 90's in population genetics. Early work aimed to estimate demographic parameters using different population models. For this reason, the existing computer packages that perform ABC (e.g. SerialSimCoal, msBayes, DIY-ABC, popABC) were developed mostly to be applied to population biology. As ABC matured and its efficiency and robustness were recognized its popularity increased and the usage of the method expanded greatly. At first, ABC spread mostly to fields related to population genetics, such as, phylogeography, conservation genetics and epidemiologic studies. At present, only 10 years since its first application, the method has already spread to a vaster variety of fields, for example, theoretical statistics, protein structure evolution, stereology, chromosomal evolution, biochemical signaling pathways, meteorology and hatching management.Despite the intensification of its usage, the statistical potential of this method is far from being reached. Indeed, although the core algorithm of ABC methods is fairly well established, modifications to widening its application and increase its efficiency have been proposed. Researchers have suggested sophisticated methodologies such as sequential approaches and hierarchical Bayesian methods, as well as, improvements on conditional density estimations, making ABC one of the most promising and fast-developing statistical techniques of the moment. The possibilities of ABC usage are also far from being fulfilled. Until now most of ABC applications have been in Natural Science, whereas fields that commonly use Bayesian applications, for example Finance, Health and Social sciences or Engineering, are yet to get the most out of this novel method. In order to bridge such gap and to increase the use of ABC there is a need for computer scientists to get more involved and to use their expertise to produce flexible user-friendly computer packages allowing more researchers from a wide variety of fields to use this recently developed statistical tool.