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Using Stacking to Average Bayesian Predictive Distributions (with Discussion)
Open accessAbstract
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.
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“On the other hand, stacking is not widely used in Bayesian model combination because the classical stacking only works with point estimates, not the entire posterior distribution (Hoeting et al., 1999).”
MethodAIC model selection using Akaike weights
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Automatic differentiation variational inference
Kucukelbir, A., Tran, D., Ranganath, R., Gelman, A., & Blei, D. M. (2016) · arXiv · doi:10.48550/arxiv.1603.00788 · Cited by 515
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rstanarm: Bayesian Applied Regression Modeling via Stan
Gabry, J., & Goodrich, B. (2016) · CRAN: Contributed Packages · doi:10.32614/cran.package.rstanarm · Cited by 503
Socioeconomic status determines COVID-19 incidence and related mortality in Santiago, Chile
Mena, G. E., Martinez, P. P., Mahmud, A. S., Marquet, P. A., Buckee, C. O., & Santillana, M. (2021) · Science · doi:10.1126/science.abg5298 · Cited by 431
loo: Efficient Leave-One-Out Cross-Validation and WAIC for Bayesian Models
Vehtari, A., Gabry, J., Magnusson, M., Yao, Y., Bürkner, P.-C., Paananen, T., & Gelman, A. (2015) · CRAN: Contributed Packages · doi:10.32614/cran.package.loo · Cited by 357
Self-citationForecast combinations: An over 50-year review
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Metadata
- Authors
- Yao, Y., Vehtari, A., Simpson, D., & Gelman, A.
- Venue
- Bayesian Analysis
- Publisher
- Institute of Mathematical Statistics
- Published
- 2018-09-01
- Volume
- 13
- Issue
- 3
- Pages
- 917-1007
- ISSN
- 1931-6690 (ISSN-L)
- 1936-0975
- OpenAlex
- W2605947465
- Cited by
- 493
- References
- 5
- FWCI
- 36.08
- Type
- journal article
- Language
- en
- Open access
- diamond
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