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We present a nonparametric Bayesian method for tting unsmooth functions which i s b a s e d o n 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 a s 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.

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We present a methodology for Bayesian model choice and averaging in Gaussian directed acyclic graphs (dags). The dimension-changing move involves adding or dropping a (directed) edge from the graph. The methodology employs the results in Geiger and Heckerman and searches directly in the space of all dags. Model determination is carried out by implementing a reversible jump Markov Chain Monte Carlo sampler. To achieve this aim we rely on the concept of adjacency matrices, which provides a relatively inexpensive check for acyclicity. The performance of our procedure is illustrated by means of two simulated datasets, as well as one real dataset.

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