We will discuss Bayesian analysis of linear-ill posed problems
with Gaussian priors and additive Gaussian noise in a separable Hilbert
space setting. Our main concerns will be wellposedness and also
contraction rates of the posterior measure as the noise goes to zero. We
will present results for mildly and severely ill-posed problems in cases
when the eigenbases of the operator to be inverted and prior are not 
simultaneously diagnolizable.