B0999
Title: Nonparametric smoothing with Markov random fields and shrinkage priors
Authors: James Faulkner - National Oceanic and Atmospheric Administration (United States) [presenting]
Abstract: A locally-adaptive nonparametric curve fitting method is presented that operates on similar principles as structured variable selection. 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 representation of shrinkage priors, we represent our method as a form of $kth$-order Markov random field smoothing. This formulation offers computational advantages and allows the application of our method where Gaussian Markov random fields have previously been used. We use Hamiltonian Monte Carlo for posterior inference because it 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 discuss a few extensions of the models, including an extension to the two-dimensional spatial setting.
