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A central statistical goal is to choose between alternative explanatorymodels of data. In many modern applications, such as population genetics, it isnot possible to apply standard methods based on evaluating the likelihoodfunctions of the models, as these are numerically intractable. ApproximateBayesian computation (ABC) is a commonly used alternative for such situations.ABC simulates data x for many parameter values under each model, which iscompared to the observed data xobs. More weight is placed on models under whichS(x) is close to S(xobs), where S maps data to a vector of summary statistics.Previous work has shown the choice of S is crucial to the efficiency andaccuracy of ABC. This paper provides a method to select good summary statisticsfor model choice. It uses a preliminary step, simulating many x values from allmodels and fitting regressions to this with the model as response. Theresulting model weight estimators are used as S in an ABC analysis. Theoreticalresults are given to justify this as approximating low dimensional sufficientstatistics. A substantive application is presented: choosing between competingcoalescent models of demographic growth for Campylobacter jejuni in New Zealandusing multi-locus sequence typing data.

Semi-automatic selection of summary statistics for ABC model choice