Simulation-based Bayesian Analysis of Complex Data

Our ability to collect large datasets is growing rapidly. Such richness of data offers great promise in terms of addressing detailed scientific questions in great depth. However, this benefit is not without scientific difficulty: many traditional analysis methods become computationally intractable for very large datasets. However, one can frequently still simulate data from scientific models for which direct calculation is no longer possible. In this paper we propose a Bayesian perspective for such analyses, and argue for the advantage of a simulation-based approximate Bayesian method that remains tractable when tractability of other methods is lost. This method, which is known as "approximate Bayesian computation" [ABC], has now been used in a variety of contexts, such as the analysis of tumor data (a tumor being a complex population of cells), and the analysis of human genetic variation data (which arise from a population of individual people). We review a number of ABC methods, with specific attention to the use of ABC in agent-based models, and give pointers to software that allows straightforward implementation of the ABC approach. In this way we demonstrate the utility of simulation-based analyses of large datasets within a rigorous statistical framework.