Considerate Approaches to Achieving Sufficiency for ABC Model Selection

ABC methods have gained popularity in situations where traditional methods which involve explicit evaluation of likelihoods are either too cumbersome or fail outright. This, almost by definition means that for any interesting real-world scenario we have no or little recourse to sufficient statistics, which had previously been central to ABC approaches and their derivation. In the context of model selection this can have particularly undesirable consequences if we have to compress the data through the use of summary statistics. In this talk we discuss complementary approaches that allow us to address this problem in a principled manner, and outline the scenarios where ABC model selection is unproblematic. We will argue that many of the most interesting applications of ABC do not use summary statistics, and that in other cases it is possible to achieve sufficiency through judicious combination of different statistics, or use of empirical likelihoods.