Deconvolution and credible intervals using Markov chain Monte Carlo method

In certain applications, e.g. during reconstruction of pulsatile hormone secretion, the traditional deterministic deconvolution techniques fail primarily due to ill conditioning. To overcome these problems, deconvolution was formulated using a stochastic approach within the Bayesian modelling framework, The stochastic deconvolution with a piece-wise constant definition of the signal (the input function) cannot be solved analytically but the solution was found by employing Markov chain Monte Carlo method. A computationally efficient sampling algorithm combined with a discrete eleconvolution method was employed. An example analysis demonstrated the application of the stochastic deconvolution method to the estimation of hormone (insulin) secretion.