Merging subposteriors becomes a regression: sample-only aggregation cuts HIGGS merge time to 0.0122 minutes

Merging several independently computed sub-sample inferences can now be done from draws of the component distributions alone, without writing down or evaluating the product density. Earlier routes either approximated each component with a parametric family and multiplied analytically, reweighted subposterior draws, or built a fusion sampler targeting the product distribution. On 11 million simulated collision events in HIGGS, splitting the data into batches and merging them gave an estimation error of 0.0020 with a merge cost of 0.0122 minutes, about 10% of full-data MCMC in total runtime.

The method represents the product distribution as the distribution of a consensus value conditional on a discrepancy being zero, then regresses that conditional mean and evaluates it at zero discrepancy. The consensus is a summary of the component draws and the discrepancy measures how far apart they are; both are computed from draws, so no density values are needed. In simulations the component family, separation, sample size, dimension and number of components were varied, with three implementations using least squares, a multilayer perceptron and Gaussian process regression, averaged over 20 replications.

The regression is given a fully Bayesian form that yields posterior variance and credible intervals covering both Monte Carlo and epistemic error. Existing approaches typically report only a Monte Carlo error, and when components are well separated their intervals shrink as particle count grows even if the estimate is inaccurate. In a Gaussian example with increasing component separation, PMC-GP posterior uncertainty grows; in the coverage experiment PMC-GP intervals give reasonable frequentist coverage while GBF intervals become increasingly undercovered as particles increase.

The method targets researchers and engineers who must merge several independently computed inferences, and it applies when each component distribution can be sampled independently and components are independent of one another. The demonstrated scope covers simulated data plus a privacy-restricted respiratory clinical trial, large-scale HIGGS inference and simulated-inference protein imaging on HSP90. The authors recommend integrating PMC and its diagnostics into a principled workflow for subsampling and aggregation, and note that when component overlap is limited one should sample from the full target when feasible or redesign the components to improve overlap.

Limited component overlap reduces the local effective sample size near zero discrepancy, making aggregation more reliant on extrapolation, as quantified by the convergence-rate result and the corresponding proposition. The authors note that large posterior uncertainty or failed posterior predictive checks then warn that the samples may not support reliable estimation. Batching also involves a tradeoff: smaller batches reduce local sampling cost but can yield more divergent subposteriors, while larger batches improve overlap at greater sampling cost. The HSP90 image simulator is third-party software that the authors do not have permission to redistribute, so the complete pipeline cannot be reproduced from the code repository alone.