Using Stacking to Average Bayesian Predictive Distributions (with Discussion)

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Journal Title
Journal ISSN
Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Date
2018-09
Major/Subject
Mcode
Degree programme
Language
en
Pages
87
917-1003
Series
Bayesian Analysis, Volume 13, issue 3
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.
Description
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
Other note
Citation
Yao , Y , Vehtari , A , Simpson , D & Gelman , A 2018 , ' Using Stacking to Average Bayesian Predictive Distributions (with Discussion) ' , Bayesian Analysis , vol. 13 , no. 3 , pp. 917-1003 . https://doi.org/10.1214/17-BA1091