Locally Adaptive Smoothing with Markov Random Fields and Shrinkage Priors

Bayesian Analysis
James R Faulkner, Vladimir N Minin

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 ...Continue Reading

References

Dec 29, 2007·Environmetrics·Christopher J Paciorek, Mark J Schervish
Dec 8, 2009·Biostatistics·Youyi FongJon Wakefield
Jan 1, 2013·Journal of the American Statistical Association·Bin Zhu, David B Dunson
Mar 29, 2016·Journal of the American Statistical Association·Anirban BhattacharyaDavid B Dunson
May 15, 2018·Bayesian Analysis·James R Faulkner, Vladimir N Minin

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Citations

Nov 30, 2019·The Journal of Animal Ecology·Nicholas M Fountain-JonesMeggan E Craft
Nov 30, 2018·Frontiers in Microbiology·Bing MaRose M Viscardi
Jul 12, 2019·Statistics in Medicine·Leonardo S BastosClaudia T Codeço
Oct 9, 2020·American Journal of Perinatology·Kristin D GersonHeather H Burris
Oct 29, 2020·PLoS Computational Biology·Andrew F MageeVladimir N Minin
May 15, 2018·Bayesian Analysis·James R Faulkner, Vladimir N Minin

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