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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Vydáno v:	Journal of the American Statistical Association Ročník 115; číslo 531; s. 1349 - 1360
Hlavní autoři:	Li, Meng, Dunson, David B.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	United States Taylor & Francis 02.07.2020 Taylor & Francis Ltd
Témata:	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
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Shrnutí:	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.
Bibliografie:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 content type line 23
ISSN:	0162-1459 1537-274X 1537-274X
DOI:	10.1080/01621459.2019.1611140