Using Stacking to Average Bayesian Predictive Distributions (with Discussion)

Yuling Yao*, Aki Vehtari, Daniel Simpson, Andrew Gelman

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

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Abstract

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.

Original languageEnglish
Pages (from-to)917-1003
Number of pages87
JournalBayesian Analysis
Volume13
Issue number3
DOIs
Publication statusPublished - Sep 2018
MoE publication typeA1 Journal article-refereed

Keywords

  • Bayesian model averaging
  • model combination
  • proper scoring rule
  • predictive distribution
  • stacking
  • Stan
  • PROPER SCORING RULES
  • CROSS-VALIDATION
  • MODEL SELECTION
  • VARIABLE SELECTION
  • COVARIATE SHIFT
  • ASYMPTOTIC EQUIVALENCE
  • INFORMATION CRITERION
  • PARETO DISTRIBUTION
  • LINEAR-REGRESSION
  • INFERENCE

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