It has been shown that ABC model choice using Bayes factors is not to be recommended due to the presence of an error coming from the use of summary statistics. The conclusion in this paper relies on the study of the behaviour of a popular method for approximating the Bayes factor (Algorithm 2).
It is well known that Bayes factors is not the only way for conducting model choice. There are other features, such as predictive performance of a model, that might be of interest (e.g. scoring rules).
My question is: is there a method, analogous to Algorithm 2, for approximating some scoring rule(s) or other quantities that can be used for conducting model choice in terms of the predictive performance in contexts with complicated likelihoods?