Now that we have a result on convergence rates based on the more general noise model, which does not rely on the triangle inequality of the fidelity functional, we can use the negative log-likelihood functional as fidelity term in the Tikhonov functional. The goal here is to estimate the solution of ill-posed problems, whose exact data is a probability density \(g^\dagger \) and the given measured data consists of realizations of random variables with distribution \(g^\dagger dx\) . We will introduce a general concentration inequality from probability theory and combine it with the convergence rates result to obtain the desired method.