On Selection of Statistics for Approximate Bayesian Computing or the Method of Simulated Moments

This paper presents a cross validation method for selection of statistics for Approximate Bayesian Computing, and for related estimation methods such as the Method of Simulated Moments. The method uses simulated annealing to minimize the cross validation criterion over a combinatorial search space that may contain many, many elements. An example, for which optimal statistics are known from theory, shows that the method is able to select optimal statistics out of a large set of candidate statistics.