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Bayesian Model Comparison with the Hyvärinen Score: Computation and Consistency

Publication ,  Journal Article
Shao, S; Jacob, PE; Ding, J; Tarokh, V
Published in: Journal of the American Statistical Association
October 2, 2019

The Bayes factor is a widely used criterion in model comparison and its logarithm is a difference of out-of-sample predictive scores under the logarithmic scoring rule. However, when some of the candidate models involve vague priors on their parameters, the log-Bayes factor features an arbitrary additive constant that hinders its interpretation. As an alternative, we consider model comparison using the Hyvärinen score. We propose a method to consistently estimate this score for parametric models, using sequential Monte Carlo methods. We show that this score can be estimated for models with tractable likelihoods as well as nonlinear non-Gaussian state-space models with intractable likelihoods. We prove the asymptotic consistency of this new model selection criterion under strong regularity assumptions in the case of nonnested models, and we provide qualitative insights for the nested case. We also use existing characterizations of proper scoring rules on discrete spaces to extend the Hyvärinen score to discrete observations. Our numerical illustrations include Lévy-driven stochastic volatility models and diffusion models for population dynamics. Supplementary materials for this article are available online.

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Published In

Journal of the American Statistical Association

DOI

EISSN

1537-274X

ISSN

0162-1459

Publication Date

October 2, 2019

Volume

114

Issue

528

Start / End Page

1826 / 1837

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 3802 Econometrics
  • 1603 Demography
  • 1403 Econometrics
  • 0104 Statistics
 

Citation

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Shao, S., Jacob, P. E., Ding, J., & Tarokh, V. (2019). Bayesian Model Comparison with the Hyvärinen Score: Computation and Consistency. Journal of the American Statistical Association, 114(528), 1826–1837. https://doi.org/10.1080/01621459.2018.1518237
Shao, S., P. E. Jacob, J. Ding, and V. Tarokh. “Bayesian Model Comparison with the Hyvärinen Score: Computation and Consistency.” Journal of the American Statistical Association 114, no. 528 (October 2, 2019): 1826–37. https://doi.org/10.1080/01621459.2018.1518237.
Shao S, Jacob PE, Ding J, Tarokh V. Bayesian Model Comparison with the Hyvärinen Score: Computation and Consistency. Journal of the American Statistical Association. 2019 Oct 2;114(528):1826–37.
Shao, S., et al. “Bayesian Model Comparison with the Hyvärinen Score: Computation and Consistency.” Journal of the American Statistical Association, vol. 114, no. 528, Oct. 2019, pp. 1826–37. Scopus, doi:10.1080/01621459.2018.1518237.
Shao S, Jacob PE, Ding J, Tarokh V. Bayesian Model Comparison with the Hyvärinen Score: Computation and Consistency. Journal of the American Statistical Association. 2019 Oct 2;114(528):1826–1837.

Published In

Journal of the American Statistical Association

DOI

EISSN

1537-274X

ISSN

0162-1459

Publication Date

October 2, 2019

Volume

114

Issue

528

Start / End Page

1826 / 1837

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 3802 Econometrics
  • 1603 Demography
  • 1403 Econometrics
  • 0104 Statistics