We consider the inversion of a linear operator with centered Gaussian white noise by MAP estimation with a Gaussian prior distribution on the solution. The actual estimator is computed approximately by a numerical method. We propose a relation between the stationarity measure of this approximate solution to the mean square error of the exact solution. This relation enables the formulation of a stopping test for the numerical method, met only by iterates that satisfy chosen statistical properties. We extend this development to Gibbs priors using a quadratic extrapolation of the log-likelihood.
Rapport technique EPM-RT-2009-10 de l'École Polytechnique de Montréal, Montréal, Canada, september 2009