Bayesian variable selection and regularization for time–frequency surface estimation

Summary. We describe novel Bayesian models for time–frequency inverse modelling of non‐stationary signals. These models are based on the idea of a Gabor regression, in which a time series is represented as a superposition of translated, modulated versions of a window function exhibiting good time–frequency concentration. As a necessary consequence, the resultant set of potential predictors is in general overcomplete—constituting a frame rather than a basis—and hence the resultant models require careful regularization through appropriate choices of variable selection schemes and prior distributions. We introduce prior specifications that are tailored to representative time series, and we develop effective Markov chain Monte Carlo methods for inference. To highlight the potential applications of such methods, we provide examples using two of the most distinctive time–frequency surfaces—speech and music signals—as well as standard test functions from the wavelet regression literature.