Function estimation with locally adaptive dynamic models

We present a nonparametric Bayesian method for fitting unsmooth
functions which is based on a locally adaptive hierarchical
extension of standard dynamic or state space models. The main idea
is to introduce locally varying variances in the states equations
and to add a further smoothness prior for this variance function.
Estimation is fully Bayesian and carried out by recent MCMC
techniques. The whole approach can be understood as an alternative
to other nonparametric function estimators, such as local
regression with local bandwidth or smoothing parameter selection.
Performance is illustrated with simulated data, including unsmooth
examples constructed for wavelet shrinkage, and by an application
to CP6 sales data.