Bayesian Fusion: Scalable unification of distributed statistical analyses

There has recently been considerable interest in addressing the problem of unifying distributed statistical analyses into a single coherent inference. This naturally arises number situations, including big-data settings, when working under privacy constraints, and Bayesian model choice. The majority existing approaches have relied upon convenient approximations analyses. Although typically being computationally efficient, readily scaling with respect to unified, approximate can significant shortcomings -- quality inference degrade rapidly be substantially biased even small that do not concur. In contrast, recent Fusion approach Dai et al. (2019) is rejection sampling scheme which parallelisable exact (avoiding any form approximation other than Monte Carlo error), albeit limited applicability low-dimensional this paper we introduce practical approach. We extend theory underpinning methodology and, by embedding it within sequential algorithm, are able recover correct target distribution. By means extensive guidance on implementation approach, demonstrate theoretically empirically robust increasing numbers analyses, coherently achieved while competitive schemes.