Alexandra Posekany (WU Vienna University of Economics and Business): Merging parallel MCMC output for horizontally partitioned data

Horizontally partitioned data frequently occur when different entities cannot pool or share their data, often due to privacy protection. A similar issue occurs, if data are too large to be analysed within a single analysis due to the computational burden. Here, we look for a way to partition the data and perform independent analyses in parallel on each partition of a size which the system can still handle. For both scenarios, combining the independently obtained results again in order to obtain a common result (posterior estimators or decisions) is far from trivial. We propose two resampling schemes, building on the samples of independent MCMC runs obtained for partitioned data in order to provide a posterior estimator comparable to the one for the full data set. To demonstrate our approaches, we simulate linear regression and economical data and show the strength of resampling in the era of parallel computation.