Nonlinearity is ubiquitous in the relationship between production data and reservoir properties. In most cases, it makes the posterior pdf for inverse problems non-GaussianNon-Gaussian pdf, so data assimilation methods that work for linear problems may not be suitable. As discussed in the previous chapters, we can classify the ensemble-based data assimilation methods into two distinct families: the MDA family that repeatedly assimilates the same data many times but with inflated observation error, and the iterative ensembles smoother based on minimization of stochastic objective functions. Both methods provide approximate sampling when the data assimilationData assimilation problem is nonlinear, but the approximation type differs. In this chapter, we examine the sampling properties for a range of degrees of nonlinearityNonlinearity to better understand the methods’ limitations.