Using stacking to average bayesian predictive distributions (with discussion)
File(s)
Published version
Author(s)
Type
Journal Article
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.
Date Issued
2018-01-01
Date Acceptance
2018-01-01
Citation
Bayesian Analysis, 2018, 13 (3), pp.917-1003
ISSN
1931-6690
Publisher
International Society for Bayesian Analysis
Start Page
917
End Page
1003
Journal / Book Title
Bayesian Analysis
Volume
13
Issue
3
Copyright Statement
©2018 International Society for Bayesian Analysis
Identifier
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000444826000001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
Subjects
Science & Technology
Physical Sciences
Mathematics, Interdisciplinary Applications
Statistics & Probability
Mathematics
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
Publication Status
Published
Date Publish Online
2018-01-16