Bayesian interpretation of periodograms

The usual nonparametric approach to spectral analysis is revisited within the regularization framework, Both usual and windowed periodograms are obtained as the squared modulus of the minimizer of regularized least squares criteria. Then, particular attention is paid to their interpretation within the Bayesian statistical framework, Finally, the question of unsupervised hyper-parameter and window selection is addressed, It is shown that maximum likelihood solution is both formally achievable and practically useful.