The first step of the parameter inference is to find the parameters maximizing the posterior. This corresponds to finding the best combination of estimators (θ: r 1 and r 2 in our specific case) which best describes the data set. This approach approach is related to well-known regression of data which is often used in chemistry. Here, the sum of squares are minimized to find the best set of fitting parameters. In the case of the likelihood distribution, we are looking for the maximum to find the best estimators ( θ: r 1,best and r 2,best ). If we choose an uninformative or flat prior one can just maximize the likelihood since the evidence (the measured data f 2 and F 2 ), p(D), does not depend on the parameters. The corresponding estimator, θ, is therefore called the maximum likelihood estimator (MLE) which are those parameters, θ satisfying