  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.
