Bayesian function learning using MCMC methods

The paper deals with the problem of reconstructing a continuous 1D function from discrete noisy samples. The measurements may also be indirect in the sense that the samples may be the output of a linear operator applied to the function. Bayesian estimation provides a unified treatment of this class of problems. We show that a rigorous Bayesian solution can be efficiently implemented by resorting to a Markov chain Monte Carlo (MCMC) simulation scheme. In particular, we discuss how the structure of the problem can be exploited in order to improve the computational and convergence performances. The effectiveness of the proposed scheme is demonstrated on two classical benchmark problems as well as on the analysis of IVGTT (IntraVenous glucose tolerance test) data, a complex identification-deconvolution problem concerning the estimation of the insulin secretion rate following the administration of an intravenous glucose injection