Various embodiments are generally directed to techniques for producing statistically correct and efficient combinations of multiple simulated posterior samples from MCMC and related Bayesian sampling schemes are described. One or more chains from a Bayesian posterior distribution of values may be generated. It may be determine whether the one or more chains have reached stationarity through parallel processing on a plurality of processing nodes. Based upon the determination, each of the one or more chains that have reached stationarity through parallel processing on the plurality of processing nodes may be sorted. The one or more sorted chains may be resampled through parallel processing on the plurality of processing nodes. The one or more resampled chains may be combined. Other embodiments are described and claimed.