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Data augmentation for non-Gaussian regression models using variance-mean mixtures

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  • N. G. Polson
  • J. G. Scott

Abstract

We use the theory of normal variance-mean mixtures to derive a data-augmentation scheme for a class of common regularization problems. This generalizes existing theory on normal variance mixtures for priors in regression and classification. It also allows variants of the expectation-maximization algorithm to be brought to bear on a wider range of models than previously appreciated. We demonstrate the method on several examples, focusing on the case of binary logistic regression. We also show that quasi-Newton acceleration can substantially improve the speed of the algorithm without compromising its robustness. Copyright 2013, Oxford University Press.

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  • N. G. Polson & J. G. Scott, 2013. "Data augmentation for non-Gaussian regression models using variance-mean mixtures," Biometrika, Biometrika Trust, vol. 100(2), pages 459-471.
    • Handle: RePEc:oup:biomet:v:100:y:2013:i:2:p:459-471
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    File URL: http://hdl.handle.net/10.1093/biomet/ass081
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    Cited by:

    1. Anindya Bhadra & Jyotishka Datta & Nicholas G. Polson & Brandon T. Willard, 2020. "Global-Local Mixtures: A Unifying Framework," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(2), pages 426-447, August.
    2. Tomohiro Ando & Jushan Bai, 2020. "Quantile Co-Movement in Financial Markets: A Panel Quantile Model With Unobserved Heterogeneity," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(529), pages 266-279, January.
    3. Nicholas G. Polson & James G. Scott, 2016. "Mixtures, envelopes and hierarchical duality," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(4), pages 701-727, September.
    4. Onizuka, Takahiro & Iwashige, Fumiya & Hashimoto, Shintaro, 2024. "Bayesian boundary trend filtering," Computational Statistics & Data Analysis, Elsevier, vol. 191(C).

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