Bayesian function learning using MCMC methods

The paper deals with the problem of reconstructing a continuous one-dimensi onal function from discrete noisy samples. The measurements may also be ind irect in the sense that the samples may be the output of a linear operator applied to the function (linear inverse problem, deconvolution). In some ca ses, the linear operator could even contain unknown parameters that are est imated from a second experiment (joint identification-deconvolution problem ). Bayesian estimation provides a unified treatment of this class of proble ms, but the practical calculation of posterior densities leads to analytica lly intractable integrals. In the paper it is shown that a rigourous Bayesi an solution can be efficiently implemented by resorting to a MCMC (Markov c hain Monte Carte) simulation scheme. In particular, it is discussed how the structure of the problem can be exploited in order to improve computationa l and convergence performances. The effectiveness of the proposed scheme is demonstrated on two classical benchmark problems as well as on the analysi s of IVGTT (IntraVenous Glucose Tolerance Test) data, a complex identificat ion-deconvolution problem concerning the estimation of the insulin secretio n rate following the administration of an intravenous glucose injection.