  In this paper we propose a general method to derive an upper bound for the
contraction rate of the posterior distribution for nonparametric inverse
problems. We present a general theorem that allows us to derive con- traction
rates for the parameter of interest from contraction rates of the related
direct problem of estimating transformed parameter of interest. An interesting
aspect of this approach is that it allows us to derive con- traction rates for
priors that are not related to the singular value decomposition of the
operator. We apply our result to several examples of linear inverse problems,
both in the white noise sequence model and the nonparametric regression model,
using priors based on the singular value decomposition of the operator,
location-mixture priors and splines prior, and recover minimax adaptive
contraction rates.
