Open Access
September 2018 Using Stacking to Average Bayesian Predictive Distributions (with Discussion)
Yuling Yao, Aki Vehtari, Daniel Simpson, Andrew Gelman
Bayesian Anal. 13(3): 917-1007 (September 2018). DOI: 10.1214/17-BA1091


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.


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Yuling Yao. Aki Vehtari. Daniel Simpson. Andrew Gelman. "Using Stacking to Average Bayesian Predictive Distributions (with Discussion)." Bayesian Anal. 13 (3) 917 - 1007, September 2018.


Published: September 2018
First available in Project Euclid: 16 January 2018

zbMATH: 06989973
MathSciNet: MR3853125
Digital Object Identifier: 10.1214/17-BA1091

Keywords: Bayesian model averaging , model combination , predictive distribution , proper scoring rule , stacking , Stan

Vol.13 • No. 3 • September 2018
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