First, a maximum-likelihood principle, based on the idea to increase the probability of successful candidate solutions and search steps. The mean of the distribution is updated such that the likelihood of previously successful candidate solutions is maximized. The covariance matrix of the distribution is updated (incrementally) such that the likelihood of previously successful search steps is increased. Both updates can be interpreted as a natural gradient descent. Also, in consequence, the CMA conducts an iterated principal components analysis of successful search steps while retaining "all" principal axes. Estimation of distribution algorithms and the Cross-Entropy Method are based on very similar ideas, but estimate (non-incrementally) the covariance matrix by maximizing the likelihood of successful solution "points" instead of successful search "steps".