Techniques for producing statistically correct and efficient combinations of multiple simulated posterior samples

A computer-implemented method, comprising:

• coordinating, at a coordinating device of a distributed system, a generation of multiple chains by a plurality of processing nodes of the distributed system from a Bayesian posterior distribution of values, wherein each processing node of the plurality of processing nodes generates one or more chains of the multiple chains independently of and at least partially in parallel with other processing nodes of the plurality of processing nodes;
• coordinating, at the coordinating device, a determination by the plurality of processing nodes of whether each chain of the multiple chains has reached stationarity, wherein each processing node of the multiple processing nodes determines whether each chain of the one or more chains generated by the processing node have reached stationarity independently of and at least partially in parallel with other processing nodes of the plurality of processing nodes;
• coordinating, at the coordinating device, a sorting of a subset of the multiple chains that have reached stationarity by the plurality of processing nodes, wherein each processing node of the plurality of processing nodes sorts each chain of the one or more chains generated by the processing node, and that is determined to have reached stationarity, based on a value of an un-normalized probability density associated with a sampled point independently of and at least partially in parallel with other processing nodes of the plurality of processing nodes;
• coordinating, at the coordinating device, a resampling with weighting of the subset of the multiple chains by the plurality of processing devices, wherein each processing node of the plurality of processing nodes assigns weights proportional to the posterior distribution to each chain of the one or more chains generated by the processing node, and that has been sorted by the processing node, during the resampling independently of and at least partially in parallel with other processing nodes of the plurality of processing nodes;
• and
• combining, at the coordinating device, the chains of the subset of the multiple chains after the resampling.

An apparatus comprising a processor and a storage to store instructions that, when executed by the processor, cause the processor to perform operations comprising:

• coordinate, at a coordinating device of a distributed system, a generation of multiple chains by a plurality of processing nodes of the distributed system from a Bayesian posterior distribution of values, wherein each processing node of the plurality of processing nodes generates one or more chains of the multiple chains independently of and at least partially in parallel with other processing nodes of the plurality of processing nodes;
• coordinate, at the coordinating device, a determination by the plurality of processing nodes of whether each chain of the multiple chains has reached stationarity, wherein each processing node of the plurality of processing nodes determines whether each chain of the one or more chains generated by the processing node have reached stationarity independently of and at least partially in parallel with other processing nodes of the plurality of processing nodes;
• coordinate, at the coordinating device, a sorting of a subset of the multiple chains that have reached stationarity by the plurality of processing nodes, wherein each processing node of the plurality of processing nodes sorts each chain of the one or more chains generated by the processing node, and that is determined to have reached stationarity, based on a value of an un-normalized probability density associated with a sampled point independently of and at least partially in parallel with other processing nodes of the plurality of processing nodes;
• coordinate, at the coordinating device, a resampling with weighting of the subset of the multiple chains by the plurality of processing nodes, wherein each processing node of the plurality of processing nodes assigns weights proportional to the posterior distribution to each chain of the one or more chains generated by the processing node, and that has been sorted by the processing node, during the resampling independently of and at least partially in parallel with other processing nodes of the plurality of processing nodes;
• and
• combine, at the coordinating device, the chains of the subset of the multiple chains after the resampling.