Using Stacking to Average Bayesian Predictive Distributions (with Discussion)

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Using Stacking to Average Bayesian Predictive Distributions (with Discussion). / Yao, Yuling; Vehtari, Aki; Simpson, Daniel; Gelman, Andrew.

In: Bayesian Analysis, Vol. 13, No. 3, 09.2018, p. 917-1003.

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Yao, Yuling ; Vehtari, Aki ; Simpson, Daniel ; Gelman, Andrew. / Using Stacking to Average Bayesian Predictive Distributions (with Discussion). In: Bayesian Analysis. 2018 ; Vol. 13, No. 3. pp. 917-1003.

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@article{063a5c3c8d5e439bac7a86702555a65f,
title = "Using Stacking to Average Bayesian Predictive Distributions (with Discussion)",
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.",
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",
author = "Yuling Yao and Aki Vehtari and Daniel Simpson and Andrew Gelman",
year = "2018",
month = "9",
doi = "10.1214/17-BA1091",
language = "English",
volume = "13",
pages = "917--1003",
journal = "Bayesian Analysis",
issn = "1936-0975",
number = "3",

}

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TY - JOUR

T1 - Using Stacking to Average Bayesian Predictive Distributions (with Discussion)

AU - Yao, Yuling

AU - Vehtari, Aki

AU - Simpson, Daniel

AU - Gelman, Andrew

PY - 2018/9

Y1 - 2018/9

N2 - 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.

AB - 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.

KW - Bayesian model averaging

KW - model combination

KW - proper scoring rule

KW - predictive distribution

KW - stacking

KW - Stan

KW - PROPER SCORING RULES

KW - CROSS-VALIDATION

KW - MODEL SELECTION

KW - VARIABLE SELECTION

KW - COVARIATE SHIFT

KW - ASYMPTOTIC EQUIVALENCE

KW - INFORMATION CRITERION

KW - PARETO DISTRIBUTION

KW - LINEAR-REGRESSION

KW - INFERENCE

U2 - 10.1214/17-BA1091

DO - 10.1214/17-BA1091

M3 - Article

VL - 13

SP - 917

EP - 1003

JO - Bayesian Analysis

JF - Bayesian Analysis

SN - 1936-0975

IS - 3

ER -

ID: 29743749