Approximate confidence distribution computing

TL;DR

Approximate confidence distribution computing (ACDC) introduces a frequentist inference method that uses confidence distributions, connecting Bayesian and frequentist paradigms, with practical algorithms that outperform some existing methods in certain scenarios.

Contribution

This work identifies a matching condition for the validity of ACDC, expanding likelihood-free inference to include non-Bayesian approaches and providing a data-driven, adaptable algorithm.

Findings

ACDC can outperform approximate Bayesian computing methods in some cases.

Theoretical validation of ACDC's frequentist validity.

Practical algorithms for Bayesian and frequentist inference using ACDC.

Abstract

Approximate confidence distribution computing (ACDC) offers a new take on the rapidly developing field of likelihood-free inference from within a frequentist framework. The appeal of this computational method for statistical inference hinges upon the concept of a confidence distribution, a special type of estimator which is defined with respect to the repeated sampling principle. An ACDC method provides frequentist validation for computational inference in problems with unknown or intractable likelihoods. The main theoretical contribution of this work is the identification of a matching condition necessary for frequentist validity of inference from this method. In addition to providing an example of how a modern understanding of confidence distribution theory can be used to connect Bayesian and frequentist inferential paradigms, we present a case to expand the current scope of so-called approximate Bayesian inference to include non-Bayesian inference by targeting a confidence distribution rather than a posterior. The main practical contribution of this work is the development of a data-driven approach to drive ACDC in both Bayesian or frequentist contexts. The ACDC algorithm is data-driven by the selection of a data-dependent proposal function, the structure of which is quite general and adaptable to many settings. We explore two numerical examples that both verify the theoretical arguments in the development of ACDC and suggest instances in which ACDC outperform approximate Bayesian computing methods computationally.