  We derive a parallel sampling algorithm for computational inverse problems
that present an unknown linear forcing term and a vector of nonlinear
parameters to be recovered. It is assumed that the data is noisy and that the
linear part of the problem is ill-posed. The vector of nonlinear parameters m
is modeled as a random variable. A dilation parameter alpha is used to scale
the regularity of the linear unknown and is also modeled as a random variable.
A posterior probability distribution for (m; alpha) is derived following an
approach related to the maximum likelihood regularization parameter selection
[5]. A major difference in our approach is that, unlike in [5], 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 [4]. This algorithm is
well-suited to problems where proposals are expensive to compute. We then apply
it to an inverse problem in seismology. We show how our results compare
favorably to those obtained from the Maximum Likelihood (ML), the Generalized
Cross Validation (GCV), and the Constrained Least Squares (CLS) algorithms.
