A Comparison of Likelihood-Free Methods With and Without Summary Statistics

TL;DR

This paper reviews and empirically compares likelihood-free methods that use full data distances versus those that rely on summary statistics, providing guidance for practitioners and highlighting promising approaches.

Contribution

It offers the first comprehensive qualitative and empirical comparison of full data distance based likelihood-free methods against summary statistic based methods.

Findings

Full data distance methods are promising but problem-dependent.

Summary statistic methods can lead to information loss.

Full data approaches warrant further development.

Abstract

Likelihood-free methods are useful for parameter estimation of complex models with intractable likelihood functions for which it is easy to simulate data. Such models are prevalent in many disciplines including genetics, biology, ecology and cosmology. Likelihood-free methods avoid explicit likelihood evaluation by finding parameter values of the model that generate data close to the observed data. The general consensus has been that it is most efficient to compare datasets on the basis of a low dimensional informative summary statistic, incurring information loss in favour of reduced dimensionality. More recently, researchers have explored various approaches for efficiently comparing empirical distributions in the likelihood-free context in an effort to avoid data summarisation. This article provides a review of these full data distance based approaches, and conducts the first comprehensive comparison of such methods, both qualitatively and empirically. We also conduct a substantive empirical comparison with summary statistic based likelihood-free methods. The discussion and results offer guidance to practitioners considering a likelihood-free approach. Whilst we find the best approach to be problem dependent, we also find that the full data distance based approaches are promising and warrant further development. We discuss some opportunities for future research in this space. Computer code to implement the methods discussed in this paper can be found at https://github.com/cdrovandi/ABC-dist-compare.