Inversion of seismic data relies on several “metaparameters” such as wavelet, correlation length, signal-to-noise ratio, and low frequency, which are given a priori status and have a strong influence on inversion results. Stochastic inversions provide a set of realizations of elastic parameters assuming a Gaussian distribution of the uncertainty of the prior model and of the data for a given set of metaparameters. By ignoring the possible variability of the metaparameters, the distribution of realizations provided by the stochastic inversions reveals only a limited amount of the true uncertainty of the posterior model. In a simple 1D example, the metaparameter has a key influence on the results. Uncertainty on several metaparameters can be estimated. In a real data example, changing the metaparameters can obtain a much larger diversity of the results than those provided by a stochastic inversion for a single set of parameters. Handling the uncertainty on all different parameters not only would be time consuming but also would be inefficient from an interpretation point of view. It certainly requires a new inversion strategy.