Title: Sparse and Smooth Prior for Bayesian Linear Regression with Application to ETEX Data,
Abstract: Sparsity of the solution of a linear regression model is a common
requirement, and many prior distributions have been designed for this purpose.
A combination of the sparsity requirement with smoothness of the solution is
also common in application, however, with considerably fewer existing prior
models. In this paper, we compare two prior structures, the Bayesian fused
lasso (BFL) and least-squares with adaptive prior covariance matrix (LS-APC).
Since only variational solution was published for the latter, we derive a Gibbs
sampling algorithm for its inference and Bayesian model selection. The method
is designed for high dimensional problems, therefore, we discuss numerical
issues associated with evaluation of the posterior. In simulation, we show that
the LS-APC prior achieves results comparable to that of the Bayesian Fused
Lasso for piecewise constant parameter and outperforms the BFL for parameters
of more general shapes. Another advantage of the LS-APC priors is revealed in
real application to estimation of the release profile of the European Tracer
Experiment (ETEX). Specifically, the LS-APC model provides more conservative
uncertainty bounds when the regressor matrix is not informative.