An exact Bayesian fusion algorithm will be presented, which can carry out perfect inferences for the unification of distributed data analysis. The new method uses parallel but coalesced Markov processes to drive distributed Monte Carlo draws to a Monte Carlo sample from the posterior of the full data.
Its approximate version, the sequential Bayesian fusion algorithm, can be implemented in parallel for big data analysis.
This new divide-and-conquer method will have potential application in many different statistics and data analysis areas, such as meta-analysis, Bayesian group decision theory and statistical cryptography.