ABC random forests for Bayesian parameter inference

TL;DR

This paper introduces a new likelihood-free Bayesian inference method using random forests that eliminates the need for selecting summary statistics and calibrating tolerance levels, improving robustness and efficiency.

Contribution

It proposes a novel ABC approach leveraging random forests for each parameter component, removing the need for summary statistic selection and tolerance calibration.

Findings

Method shows robustness to summary statistic choice

Eliminates the need for tolerance level calibration

Performs well on toy and real data examples

Abstract

This preprint has been reviewed and recommended by Peer Community In Evolutionary Biology (http://dx.doi.org/10.24072/pci.evolbiol.100036). Approximate Bayesian computation (ABC) has grown into a standard methodology that manages Bayesian inference for models associated with intractable likelihood functions. Most ABC implementations require the preliminary selection of a vector of informative statistics summarizing raw data. Furthermore, in almost all existing implementations, the tolerance level that separates acceptance from rejection of simulated parameter values needs to be calibrated. We propose to conduct likelihood-free Bayesian inferences about parameters with no prior selection of the relevant components of the summary statistics and bypassing the derivation of the associated tolerance level. The approach relies on the random forest methodology of Breiman (2001) applied in a (non parametric) regression setting. We advocate the derivation of a new random forest for each component of the parameter vector of interest. When compared with earlier ABC solutions, this method offers significant gains in terms of robustness to the choice of the summary statistics, does not depend on any type of tolerance level, and is a good trade-off in term of quality of point estimator precision and credible interval estimations for a given computing time. We illustrate the performance of our methodological proposal and compare it with earlier ABC methods on a Normal toy example and a population genetics example dealing with human population evolution. All methods designed here have been incorporated in the R package abcrf (version 1.7) available on CRAN.