Approximation Bayesian computation [ABC] is an analysis approach that has arisen in response to the recent trend to collect data that is of a magnitude far higher than has been historically the case. This has led to many existing methods become intractable because of difficulties in calculating the likelihood function. ABC circumvents this issue by replacing calculation of the likelihood with a simulation step in which it is estimated in one way or another. In this review we give an overview of the ABC approach, giving examples of some of the more popular specific forms of ABC. We then discuss some of the areas of most active research and application in the field, specifically, choice of low-dimensional summaries of complex datasets and metrics for measuring similarity between observed and simulated data. Next, we consider the question of how to do model selection in an ABC context. Finally, we discuss an area of growing prominence in the ABC world, use of ABC methods in genetic pathway inference.
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