Bayesian Analysis
- Bayesian Anal.
- Volume 13, Number 3 (2018), 917-1007.
Using Stacking to Average Bayesian Predictive Distributions (with Discussion)
Yuling Yao, Aki Vehtari, Daniel Simpson, and Andrew Gelman
Abstract
Bayesian model averaging is flawed in the -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.
Article information
Source
Bayesian Anal., Volume 13, Number 3 (2018), 917-1007.
Dates
First available in Project Euclid: 16 January 2018
Permanent link to this document
https://projecteuclid.org/euclid.ba/1516093227
Digital Object Identifier
doi:10.1214/17-BA1091
Mathematical Reviews number (MathSciNet)
MR3853125
Zentralblatt MATH identifier
06989973
Keywords
Bayesian model averaging model combination proper scoring rule predictive distribution stacking Stan
Rights
Creative Commons Attribution 4.0 International License.
Citation
Yao, Yuling; Vehtari, Aki; Simpson, Daniel; Gelman, Andrew. Using Stacking to Average Bayesian Predictive Distributions (with Discussion). Bayesian Anal. 13 (2018), no. 3, 917--1007. doi:10.1214/17-BA1091. https://projecteuclid.org/euclid.ba/1516093227
Supplemental materials
- Supplementary Material to “Using Stacking to Average Bayesian Predictive Distributions”. Digital Object Identifier: doi:10.1214/17-BA1091SUPP