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Approximate Confidence Distribution Computing
Volume 1, Issue 2 (2023), pp. 270–282
Suzanne Thornton   Wentao Li   Minge Xie  

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https://doi.org/10.51387/23-NEJSDS38
Pub. online: 4 July 2023      Type: Methodology Article      Open accessOpen Access
Area: Statistical Methodology

Accepted
24 April 2023
Published
4 July 2023

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 three 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.

Supplementary material

 Supplementary Material
The Appendices and Supplementary Material are available online. Besides detailed proofs, this material contains additional conditions and provides a few additional remarks as noted earlier in this paper.

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Keywords
Approximate Bayesian inference Confidence distribution Computational inference

Funding
The research is supported in part by research grants from the US National Science Foundation (DMS1812048, DMS2015373 and DMS2027855). This research stems from a chapter of the first author’s PhD Thesis. The first author also acknowledges the generous graduate support from Rutgers University.

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