Using Stacking to Average Bayesian Predictive Distributions (with Discussion)

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.

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

DOI

10.1214/17-BA1091

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

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https://urn.fi/URN:NBN:fi:aalto-201812105913

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[article-cris] Perustieteiden korkeakoulu / SCI

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Using Stacking to Average Bayesian Predictive Distributions (with Discussion)

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