Algorithm

Stacking

Bayesian probability

Statistics

Approximate Bayesian computation

Nuclear magnetic resonance

Stability (learning theory)

Bayesian statistics

Computation

Weighting

Computer science

Radiology

Physics

Mathematics

Inference

Artificial intelligence

Medicine

Posterior probability

Machine learning

Bayesian inference

Bayesian Analysis

Bayesian model averaging is flawed in the M-open setting in which the true data-generating process is not one of the candidate models being fit. We take the idea of stacking from the point estimation literature and generalize to the combination of predictive distributions. We extend the utility function to any proper scoring rule and use Pareto smoothed importance sampling to efficiently compute the required leave-one-out posterior distributions. We compare stacking of predictive distributions to several alternatives: stacking of means, Bayesian model averaging (BMA), Pseudo-BMA, and a variant of Pseudo-BMA that is stabilized using the Bayesian bootstrap. Based on simulations and real-data applications, we recommend stacking of predictive distributions, with bootstrapped-Pseudo-BMA as an approximate alternative when computation cost is an issue.

Using Stacking to Average Bayesian Predictive Distributions (with Discussion)