Year: 2016
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Institutions: University of South Carolina, Texas A&M University
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Institutes of Health
Award: G1917267738
OpenAlex ID: W2427448317