Misc,
Bayesian trend filtering: adaptive temporal smoothing with shrinkage priors
(2015)cite arxiv:1512.06505.
Abstract
We present a locally-adaptive nonparametric curve fitting method that we call
Bayesian trend filtering. The method operates within a fully Bayesian framework
and 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 Bayesian trend filtering and kth order
Gaussian Markov random field smoothing. 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 Bayesian trend filtering 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 efficiency to make it a useful addition to the
Bayesian nonparametric toolbox.
