Title: An effective likelihood-free approximate computing method with statistical inferential guarantees,
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.