The likelihood p(D|θ) is often denoted L(D|θ) and is in our case given by equation (12). In practice the logarithmic likelihood L -2 ln L is often minimized since it is numerically much more stable. What is done technically is to run an optimizer on L(θ) to find θ, e.g. a Nelder-Mead algorithm. The outlined procedure is in principle straightforward. However, the elephant in the room is the likelihood, how do we know how it looks like? In principle the only way to find out is to create many realizations of the same data set to obtain samples of p(D|θ). This is often unpractical and certain assumptions are made. One of the most common one is the assumption of the likelihood being a multivariate Gaussian making the life of statisticians much easier. It corresponds to least-square fitting since maximizing the log-likelihood of a Gaussian A.3 Bayes theorem, marginal and conditional probabilities corresponds to the sum of squares. Another motivation for the Gaussian distribution is the central-limit-theorem stating that any sum of independent and identically distributed random variables with finite variance tend to a Gaussian distribution.