The Hodrick-Prescott (HP) Filter as a Bayesian Regression Model

The Hodrick-Prescott (HP) method is a popular smoothing method for economic time series to get a smooth or long-term component of stationary series like growth rates. We show that the HP smoother can be viewed as a Bayesian linear model with a strong prior using differencing matrices for the smoothness component. The HP smoothing approach requires a linear regression model with a Bayesian conjugate multi-normalgamma distribution. The Bayesian approach also allows to make predictions of the HP smoother on both ends of the time series. Furthermore, we show how Bayes tests can determine the order of smoothness in the HP smoothing model. The extended HP smoothing approach is demonstrated for the non-stationary (textbook) airline passenger time series. Thus, the Bayesian extension of the HP model defines a new class of model-based smoothers for (non-stationary) time series and spatial models.Hodrick-Prescott (HP) smoothers, model selection by marginal likelihoods, multi-normal-gamma distribution, Spatial sales growth data, Bayesian econometrics

Analysis of DCE-MRI Data using a Nonnegative Elastic Net

We present a nonnegative Elastic Net approach for the analysis of Dynamic Contrast-Enhanced Magnetic Resonance Imaging data. A multi-compartment approach is considered, which is translated into a (restricted) least square model selection problem. This is done by using a set of basis functions for a given set of candidate rate constants. The form of the basis functions is derived from a kinetic model and thus describes the contribution of some compartment. Using the Elastic Net estimator, we chose clusters of basis functions, and hence, rate constants of compartments. As further challenge, the estimator has to be restricted to positive regression parameters, which correspond to transfer rates of the compartments. The proposed estimation method is applied to an in-vivo data set