A note on target distribution ambiguity of likelihood-free samplers

TL;DR

This paper discusses the ambiguity in target distribution forms when using likelihood-free samplers in Bayesian simulation, highlighting theoretical considerations and implications for future algorithm development.

Contribution

It introduces generalizations of existing likelihood-free algorithms and analyzes their potential ambiguities in target distribution specification.

Findings

Likelihood-free samplers can be ambiguous over target distribution forms.

Generalizations of existing algorithms are proposed.

Implications for future development of likelihood-free methods are discussed.

Abstract

Methods for Bayesian simulation in the presence of computationally intractable likelihood functions are of growing interest. Termed likelihood-free samplers, standard simulation algorithms such as Markov chain Monte Carlo have been adapted for this setting. In this article, by presenting generalisations of existing algorithms, we demonstrate that likelihood-free samplers can be ambiguous over the form of the target distribution. We also consider the theoretical justification of these samplers. Distinguishing between the forms of the target distribution may have implications for the future development of likelihood-free samplers.