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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| Veröffentlicht in: | Journal of the American Statistical Association Jg. 115; H. 531; S. 1349 - 1360 |
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| Sprache: | Englisch |
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Taylor & Francis
02.07.2020
Taylor & Francis Ltd |
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| Abstract | 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. |
|---|---|
| AbstractList | 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. 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.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. We propose a new approach for assigning weights to models using a divergence-based method ( ), 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. 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. 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. |
| Author | Dunson, David B. Li, Meng |
| AuthorAffiliation | 2 Department of Statistical Science, Duke University 1 Department of Statistics, Rice University |
| AuthorAffiliation_xml | – name: 1 Department of Statistics, Rice University – name: 2 Department of Statistical Science, Duke University |
| Author_xml | – sequence: 1 givenname: Meng orcidid: 0000-0003-2123-2444 surname: Li fullname: Li, Meng email: meng@rice.edu organization: Department of Statistics, Rice University – sequence: 2 givenname: David B. surname: Dunson fullname: Dunson, David B. organization: Department of Statistical Science, Duke University |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/33716357$$D View this record in MEDLINE/PubMed |
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| SubjectTerms | 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 |
| Title | Comparing and Weighting Imperfect Models Using D-Probabilities |
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