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March 2018 Locally Adaptive Smoothing with Markov Random Fields and Shrinkage Priors
James R. Faulkner, Vladimir N. Minin
Bayesian Anal. 13(1): 225-252 (March 2018). DOI: 10.1214/17-BA1050

Abstract

We present a locally adaptive nonparametric curve fitting method that operates within a fully Bayesian framework. This method uses shrinkage priors to induce sparsity in order-k differences in the latent trend function, providing a combination of local adaptation and global control. Using a scale mixture of normals representation of shrinkage priors, we make explicit connections between our method and kth order Gaussian Markov random field smoothing. We call the resulting processes shrinkage prior Markov random fields (SPMRFs). We use Hamiltonian Monte Carlo to approximate the posterior distribution of model parameters because this method provides superior performance in the presence of the high dimensionality and strong parameter correlations exhibited by our models. We compare the performance of three prior formulations using simulated data and find the horseshoe prior provides the best compromise between bias and precision. We apply SPMRF models to two benchmark data examples frequently used to test nonparametric methods. We find that this method is flexible enough to accommodate a variety of data generating models and offers the adaptive properties and computational tractability to make it a useful addition to the Bayesian nonparametric toolbox.

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James R. Faulkner. Vladimir N. Minin. "Locally Adaptive Smoothing with Markov Random Fields and Shrinkage Priors." Bayesian Anal. 13 (1) 225 - 252, March 2018. https://doi.org/10.1214/17-BA1050

Information

Published: March 2018
First available in Project Euclid: 24 February 2017

zbMATH: 06873725
MathSciNet: MR3737950
Digital Object Identifier: 10.1214/17-BA1050

Keywords: Hamiltonian Monte Carlo , horseshoe prior , Lévy process , nonparametric

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Vol.13 • No. 1 • March 2018
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