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Approximating posteriors with high-dimensional nuisance parameters via integrated rotated Gaussian approximation.

Publication ,  Journal Article
VAN DEN Boom, W; Reeves, G; Dunson, DB
Published in: Biometrika
June 2021

Posterior computation for high-dimensional data with many parameters can be challenging. This article focuses on a new method for approximating posterior distributions of a low- to moderate-dimensional parameter in the presence of a high-dimensional or otherwise computationally challenging nuisance parameter. The focus is on regression models and the key idea is to separate the likelihood into two components through a rotation. One component involves only the nuisance parameters, which can then be integrated out using a novel type of Gaussian approximation. We provide theory on approximation accuracy that holds for a broad class of forms of the nuisance component and priors. Applying our method to simulated and real data sets shows that it can outperform state-of-the-art posterior approximation approaches.

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Published In

Biometrika

DOI

EISSN

1464-3510

ISSN

0006-3444

Publication Date

June 2021

Volume

108

Issue

2

Start / End Page

269 / 282

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 3802 Econometrics
  • 1403 Econometrics
  • 0104 Statistics
  • 0103 Numerical and Computational Mathematics
 

Citation

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VAN DEN Boom, W., Reeves, G., & Dunson, D. B. (2021). Approximating posteriors with high-dimensional nuisance parameters via integrated rotated Gaussian approximation. Biometrika, 108(2), 269–282. https://doi.org/10.1093/biomet/asaa068
VAN DEN Boom, W., G. Reeves, and D. B. Dunson. “Approximating posteriors with high-dimensional nuisance parameters via integrated rotated Gaussian approximation.Biometrika 108, no. 2 (June 2021): 269–82. https://doi.org/10.1093/biomet/asaa068.
VAN DEN Boom, W., et al. “Approximating posteriors with high-dimensional nuisance parameters via integrated rotated Gaussian approximation.Biometrika, vol. 108, no. 2, June 2021, pp. 269–82. Epmc, doi:10.1093/biomet/asaa068.
VAN DEN Boom W, Reeves G, Dunson DB. Approximating posteriors with high-dimensional nuisance parameters via integrated rotated Gaussian approximation. Biometrika. 2021 Jun;108(2):269–282.

Published In

Biometrika

DOI

EISSN

1464-3510

ISSN

0006-3444

Publication Date

June 2021

Volume

108

Issue

2

Start / End Page

269 / 282

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 3802 Econometrics
  • 1403 Econometrics
  • 0104 Statistics
  • 0103 Numerical and Computational Mathematics