The skill of climate projections depends on the ability of models to reproduce the long-term and low-frequency variability of the system. It is thus important that low-frequency model statistics can be checked against observations. In this paper, a method is proposed to estimate directly the low-frequency component of the ocean variability from native observations using statistics from a prior long-term simulation. It is designed to account for possible model biases and to provide an estimate of the correction required to fit observations. The result is obtained by an MCMC sampler (modified to include localization of the model covariance), which provides an ensemble description of the solution, so that uncertainties can be properly assessed using independent data. This algorithm is shown well suited to work with MPI and GPUs, and efficient enough to solve large-size problems (about 10⁸ variables and 10⁷ observations). The approach is illustrated by the reconstruction of the low-frequency variability of the Mediterranean sea level, using statistics from a 1/12° resolution ensemble model simulation. The resulting ensemble is assessed against independent observations (by cross-validation), showing good reliability (flat rank histogram). The method also produces a consistent estimate of the model bias and of the observation error variance (mainly representativity error), while the missing prior ensemble variance is shown to be less controlable by the observations, and thus rather computed as a diagnostic. Overall, this application shows the importance of reliable model statistics, and thus the importance of enhancing model simulations to represent all main sources of uncertainty.