Comparing and Weighting Imperfect Models Using D-Probabilities

We propose a new approach for assigning weights to models using a divergence-based method (D-probabilities), relying on evaluating parametric models relative to a nonparametric Bayesian reference using Kullback-Leibler divergence. D-probabilities are useful in goodness-of-fit assessments, in compari...

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Bibliographic Details
Published in:Journal of the American Statistical Association Vol. 115; no. 531; pp. 1349 - 1360
Main Authors: Li, Meng, Dunson, David B.
Format: Journal Article
Language:English
Published: United States Taylor & Francis 02.07.2020
Taylor & Francis Ltd
Subjects:
Asymptotic properties
Atmospheric ozone
Bayesian analysis
Bayesian theory
Computer simulation
Gaussian process
Gibbs posterior
Goodness of fit
Kullback-Leibler divergence
Linear analysis
linear models
M-open
Model aggregation
Model selection
Morality
normal distribution
ozone
Property
Regression analysis
Simulation
Statistical methods
Statistics
Weighting
Gaussian process
Model selection
Nonparametric Bayes
M-open
Kullback-Leibler divergence
Model aggregation
Gibbs posterior
Posterior probabilities
ISSN:0162-1459, 1537-274X, 1537-274X
Online Access:Get full text
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Summary:We propose a new approach for assigning weights to models using a divergence-based method (D-probabilities), relying on evaluating parametric models relative to a nonparametric Bayesian reference using Kullback-Leibler divergence. D-probabilities are useful in goodness-of-fit assessments, in comparing imperfect models, and in providing model weights to be used in model aggregation. D-probabilities avoid some of the disadvantages of Bayesian model probabilities, such as large sensitivity to prior choice, and tend to place higher weight on a greater diversity of models. In an application to linear model selection against a Gaussian process reference, we provide simple analytic forms for routine implementation and show that D-probabilities automatically penalize model complexity. Some asymptotic properties are described, and we provide interesting probabilistic interpretations of the proposed model weights. The framework is illustrated through simulation examples and an ozone data application. Supplementary materials for this aricle are available online.
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ISSN:0162-1459
1537-274X
1537-274X
DOI:10.1080/01621459.2019.1611140