Bayesian Function Learning Using MCMC Methods
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Technique for the Numerical Solution of Certain Integral Equations of the First Kind
Journal of the ACM (JACM)
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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 deconvolution method was employed. An example analysis demonstrated the application of the stochastic deconvolution method to the estimation of hormone (insulin) secretion.