Supplement to “A Comparative Review of Dimension Reduction Methods in Approximate Bayesian Computation.” DOI:10.1214/12-STS406SUPP

Abstract. Approximate Bayesian computation (ABC) methods make use of comparisons between simulated and observed summary statistics to over-come the problem of computationally intractable likelihood functions. As the practical implementation of ABC requires computations based on vec-tors of summary statistics, rather than full data sets, a central question is how to derive low-dimensional summary statistics from the observed data with minimal loss of information. In this article we provide a comprehen-sive review and comparison of the performance of the principal methods of dimension reduction proposed in the ABC literature. The methods are split into three nonmutually exclusive classes consisting of best subset selection methods, projection techniques and regularization. In addition, we introduce two new methods of dimension reduction. The first is a best subset selection method based on Akaike and Bayesian information criteria, and the second uses ridge regression as a regularization procedure. We illustrate the perfor-mance of these dimension reduction techniques through the analysis of three challenging models and data sets