Using Stacking to Average Bayesian Predictive Distributions (with Discussion)

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 func...

Full description

Saved in:
Bibliographic Details
Published inBayesian analysis Vol. 13; no. 3; pp. 917 - 1003
Main Authors Yao, Yuling, Vehtari, Aki, Simpson, Daniel, Gelman, Andrew
Format Journal Article
LanguageEnglish
Published International Society for Bayesian Analysis 01.09.2018
Subjects
Computer Science
Mathematics
Bayesian model averaging
Stan
predictive distribution
model combination
proper scoring rule
stacking
Online AccessGet full text

Cover

More Information
Summary: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.
ISSN:1936-0975
1931-6690
DOI:10.1214/17-BA1091