Comparing and Weighting Imperfect Models Using D-Probabilities


Journal Article

© 2019 American Statistical Association. 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.

Full Text

Duke Authors

Cited Authors

  • Li, M; Dunson, DB

Published Date

  • July 2, 2020

Published In

Volume / Issue

  • 115 / 531

Start / End Page

  • 1349 - 1360

Electronic International Standard Serial Number (EISSN)

  • 1537-274X

International Standard Serial Number (ISSN)

  • 0162-1459

Digital Object Identifier (DOI)

  • 10.1080/01621459.2019.1611140

Citation Source

  • Scopus