Periodic components estimation in chronobiological time series via a Bayesian approach

In chronobiology a periodic components variation analysis for the signals expressing the biological rhythms is needed. Therefore precise estimation of the periodic components is required. The classical approaches, based on FFT methods, are inefficient considering the particularities of the data (non-stationary, short length and noisy). In this paper we propose a new method using inverse problem and Bayesian approach with sparsity enforcing prior. The considered prior law is the Student-t distribution, viewed as a marginal distribution of an Infinite Gaussian Scale Mixture (IGSM) defined via the inverse variances. For modelling the non stationarity of the observed signal and the noise we use a Gaussian model with unknown variances. To infer those variances as well as the variances of the periodic components we use conjugate priors. From the joint posterior law the unknowns are estimated via Posterior Mean (PM) using the Variational Bayesian Approximation (VBA). Finally, we validate the proposed method on synthetic data and present some preliminary results for real chronobiological data.