Before revision:  1992 ] , which we generalize to the case where the underlying linear operator is rectangular and depends on a nonlinear parameter . A major difference in our approach is that, unlike in [ Galatsanos and Katsaggelos, 1992 ], we do not limit ourselves to the most likely regularization parameter, instead we show that due to the dependence of the problem on the nonlinear parameter, there is a great advantage in exploring all positive values of the regularization parameter. Based on our new probability distribution function, we construct a choice sampling algorithm to compute the posterior expected value and covariance of the nonlinear parameter. This algorithm is greatly accelerated by using a parallel platform where we alternate computing proposals in parallel and combining proposals to accept or reject them as in [ Calderhead, 2014 ].
After revision:  1992 ] , which we generalize to the case where the underlying linear operator is rectangular and depends on a nonlinear parameter . A major difference in our approach is that, unlike in [ Galatsanos and Katsaggelos, 1992 ], we do not limit ourselves to the maximum likelihood value of alpha. We then derive a parallel sampling algorithm where we alternate computing proposals in parallel and combining proposals to accept or reject them as in [ Calderhead, 2014 ].