We will now introduce the so-called randomized-maximum-likelihood sampling (RML), which provides a mean for sampling the posterior distribution in cases with modest nonlinearity. The method is a randomized a posteriori sampling, but we will use the standard notation common in the literature. The RML method assumes that we obtain approximate samples from the posterior distribution by minimizing an ensemble of specific cost functions. As this sampling is exact in the linear case, it is reasonable to assume that it provides approximate samples in the weakly nonlinear case. The RML sampling provides a fundamental basis for ensemble methods and allows us to connect these methods directly to Bayes’ theorem.