An effective likelihood-free approximate computing method with statistical inferential guarantees

TL;DR

This paper introduces a likelihood-free inference method called approximate confidence distribution computing, which provides statistical guarantees and extends the applicability of approximate Bayesian computing, especially with non-sufficient statistics and data-dependent priors.

Contribution

It develops a new frequentist framework for likelihood-free inference, supporting non-sufficient statistics and data-dependent priors, with theoretical guarantees and improved computational efficiency.

Findings

The method achieves correct frequency coverage rates.

It allows the use of data-dependent priors without losing inferential validity.

Simulation studies show increased speed and broader applicability.

Abstract

Approximate Bayesian computing is a powerful likelihood-free method that has grown increasingly popular since early applications in population genetics. However, complications arise in the theoretical justification for Bayesian inference conducted from this method with a non-sufficient summary statistic. In this paper, we seek to re-frame approximate Bayesian computing within a frequentist context and justify its performance by standards set on the frequency coverage rate. In doing so, we develop a new computational technique called approximate confidence distribution computing, yielding theoretical support for the use of non-sufficient summary statistics in likelihood-free methods. Furthermore, we demonstrate that approximate confidence distribution computing extends the scope of approximate Bayesian computing to include data-dependent priors without damaging the inferential integrity. This data-dependent prior can be viewed as an initial `distribution estimate' of the target parameter which is updated with the results of the approximate confidence distribution computing method. A general strategy for constructing an appropriate data-dependent prior is also discussed and is shown to often increase the computing speed while maintaining statistical inferential guarantees. We supplement the theory with simulation studies illustrating the benefits of the proposed method, namely the potential for broader applications and the increased computing speed compared to the standard approximate Bayesian computing methods.