## ABC model choice by random forests [guest post]

*[Dennis Prangle sent me his comments on our ABC model choice by random forests paper. Here they are! And I appreciate very much contributors commenting on my paper or others, so please feel free to join.]*

**T**his paper proposes a new approach to likelihood-free model choice based on random forest classifiers. These are fit to simulated model/data pairs and then run on the observed data to produce a predicted model. A novel “posterior predictive error rate” is proposed to quantify the degree of uncertainty placed on this prediction. Another interesting use of this is to tune the threshold of the standard ABC rejection approach, which is outperformed by random forests.

The paper has lots of thought-provoking new ideas and was an enjoyable read, as well as giving me the encouragement I needed to read another chapter of the indispensable *Elements of Statistical Learning* However I’m not fully convinced by the approach yet for a few reasons which are below along with other comments.

Alternative schemes

The paper shows that random forests outperform rejection based ABC. I’d like to see a comparison to more efficient ABC model choice algorithms such as that of Toni et al 2009. Also I’d like to see if the output of random forests could be used as summary statistics within ABC rather than as a separate inference method.

**Posterior predictive error rate (PPER)**

This is proposed to quantify the performance of a classifier given a particular data set. The PPER is the proportion of times the classifier’s most favoured model is incorrect for simulated model/data pairs drawn from an approximation to the posterior predictive. The approximation is produced by a standard ABC analysis.

Misclassification could be due to (a) a poor classifier or (b) uninformative data, so the PPER aggregrates these two sources of uncertainty. I think it is still very desirable to have an estimate of the uncertainty due to (b) only i.e. a posterior weight estimate. However the PPER is useful. Firstly end users may sometimes only care about the aggregated uncertainty. Secondly relative PPER values for a fixed dataset are a useful measure of uncertainty due to (a), for example in tuning the ABC threshold. Finally, one drawback of the PPER is the dependence on an ABC estimate of the posterior: how robust are the results to the details of how this is obtained?

**Classification**

This paper illustrates an important link between ABC and machine learning classification methods: model choice can be viewed as a classification problem. There are some other links: some classifiers make good model choice summary statistics (Prangle et al 2014) or good estimates of ABC-MCMC acceptance ratios for parameter inference problems (Pham et al 2014). So the good performance random forests makes them seem a generally useful tool for ABC (indeed they are used in the Pham et al al paper).

August 29, 2014 at 4:07 pm

Some links between classification and ABC are mentioned in the last paragraph. To these, we may add our recent finding that classification accuracy can _directly_ be used as a discrepancy measure in ABC, or likelihood-free inference in general (http://arxiv.org/abs/1407.4981).

Michael and Ritabrata