Functional Horseshoe Priors for Subspace Shrinkage

We introduce a new shrinkage prior on function spaces, called the functional horseshoe (fHS) prior, that encourages shrinkage toward parametric classes of functions. Unlike other shrinkage priors for parametric models, the fHS shrinkage acts on the shape of the function rather than inducing sparsity...

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Bibliographic Details
Published in:Journal of the American Statistical Association 2020, Vol.115 (532), p.1784-1797
Main Authors: Shin, Minsuk, Bhattacharya, Anirban, Johnson, Valen E.
Format: Article
Language:English
Subjects:
Additive model
Bayesian shrinkage
Efficacy
Function space
Functionals
Mathematical models
Nonparametric regression
Nonparametric statistics
Parameters
Posterior contraction
Regression analysis
Shrinkage
Statistical methods
Statistics
Thresholds
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Summary:We introduce a new shrinkage prior on function spaces, called the functional horseshoe (fHS) prior, that encourages shrinkage toward parametric classes of functions. Unlike other shrinkage priors for parametric models, the fHS shrinkage acts on the shape of the function rather than inducing sparsity on model parameters. We study the efficacy of the proposed approach by showing an adaptive posterior concentration property on the function. We also demonstrate consistency of the model selection procedure that thresholds the shrinkage parameter of the fHS prior. We apply the fHS prior to nonparametric additive models and compare its performance with procedures based on the standard horseshoe prior and several penalized likelihood approaches. We find that the new procedure achieves smaller estimation error and more accurate model selection than other procedures in several simulated and real examples. Supplementary materials for this article, which contain additional simulated and real data examples, MCMC diagnostics, and proofs of the theoretical results, are available online.
ISSN:0162-1459
1537-274X
DOI:10.1080/01621459.2019.1654875