Simulation-based stacking

Simulation-based inference has been popular for amortized Bayesian computation. It is typical to have more than one posterior approximation, from different inference algorithms, different architectures, or simply the randomness of initialization and stochastic gradients. With a consistency guarantee, we present a general posterior stacking framework to make use of all available approximations. Our stacking method is able to combine densities, simulation draws, confidence intervals, and moments, and address the overall precision, calibration, coverage, and bias of the posterior approximation at the same time. We illustrate our method on several benchmark simulations and a challenging cosmological inference task.