that is, we marginalize over the latent variables (the true values related via the model). It is this likelihood which is maximized in by iterations through the outer and inner loop, that is finding best fit value (the maximum likelihood estimator (MLE)) for given independent variables and then find the MLE for the independent variable. This procedure is repeated until converged. One could set up a full hierarchical model by promoting the independent true variables to parameters and sampling from the full joint distribution function with Markov chain Monte Carlo (MCMC) methods. We would like to stress that this would be the correct way to proceed and that the MLE found in will be the same (the posterior distribution would still be non-Gaussian though). However, one can simplify the problem dramatically with a few assumptions which are very well satisfied in the inference of reactivity ratios.