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Approximate confidence distribution computing: An effective likelihood-free method with statistical guarantees


Approximate Bayesian computing (ABC) is a likelihood-free method that has grown increasingly popular since early applications in population genetics. However, the theoretical justification for Bayesian inference (e.g. construction of credible intervals) based on this method has not yet been fully addressed when using non-sufficient summary statistics. We introduce a more general computational technique, approximate confidence distribution computing (ACC), to overcome a few issues associated with the ABC method, for instance, the lack of theory supporting for constructing credible (or confidence) intervals when the ACC method uses non-sufficient summary statistics, the long computing time, and the necessity of a prior assumption. Specifically, we establish frequentist coverage properties for the outcome of the ACC method by using the theory of confidence distributions, and thus inference based on ACC is justified, even if reliant upon a non-sufficient summary statistic. Furthermore, the ACC method is very broadly applicable; in fact, the ABC algorithm can be viewed as a special case of an ACC method without damaging the integrity of ACC based inference. We supplement the theory with simulation studies and an epidemiological application to illustrate the benefits of the ACC method. It is demonstrated that a well-tended ACC algorithm can greatly increase its computing efficiency over a typical ABC algorithm.