A Comparative Review of Dimension Reduction Methods in Approximate Bayesian Computation

TL;DR

This paper reviews and compares various dimension reduction techniques in Approximate Bayesian Computation, introduces two new methods, and evaluates their performance on complex models to improve likelihood-free inference.

Contribution

It provides a comprehensive comparison of existing dimension reduction methods in ABC and introduces two novel approaches using information criteria and ridge regression.

Findings

New methods outperform some existing techniques in certain models

Dimension reduction significantly improves ABC efficiency

Performance varies across different models and data sets

Abstract

Approximate Bayesian computation (ABC) methods make use of comparisons between simulated and observed summary statistics to overcome the problem of computationally intractable likelihood functions. As the practical implementation of ABC requires computations based on vectors 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 comprehensive 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 performance of these dimension reduction techniques through the analysis of three challenging models and data sets.