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Sparsity of the solution of a linear regression model is a commonrequirement, and many prior distributions have been designed for this purpose.A combination of the sparsity requirement with smoothness of the solution isalso common in application, however, with considerably fewer existing priormodels. In this paper, we compare two prior structures, the Bayesian fusedlasso (BFL) and least-squares with adaptive prior covariance matrix (LS-APC).Since only variational solution was published for the latter, we derive a Gibbssampling algorithm for its inference and Bayesian model selection. The methodis designed for high dimensional problems, therefore, we discuss numericalissues associated with evaluation of the posterior. In simulation, we show thatthe LS-APC prior achieves results comparable to that of the Bayesian FusedLasso for piecewise constant parameter and outperforms the BFL for parametersof more general shapes. Another advantage of the LS-APC priors is revealed inreal application to estimation of the release profile of the European TracerExperiment (ETEX). Specifically, the LS-APC model provides more conservativeuncertainty bounds when the regressor matrix is not informative.

Sparse and Smooth Prior for Bayesian Linear Regression with Application to ETEX Data