Abstract: Inference on high-dimensional parameters in structured linear models is an important statistical problem. Focusing on the case of a piecewise polynomial Gaussian sequence model, we develop a new empirical Bayes solution that enjoys adaptive minimax posterior concentration rates and improved structure learning properties than existing methods. Moreover, the conjugate form of the empirical prior means the posterior computations are fast and easy. Numerical examples highlight the method's strong finite-sample performance compared with that of existing methods in various scenarios.

Key words and phrases: Bayesian estimation, change-point detection, high dimensional inference, structure learning, trend filtering.