Reservoir engineering studies involve a large number of parameters with great uncertainties. To ensure correct future production, a comparison of possible scenarios in managing related uncertainties is needed. Comparisons can be performed with more information than only a single mean case for each scenario. The Bayesian formalism is well tailored to address the key problem of making predictions under uncertainty, especially in mature fields. It enables to define the reservoir uncertainty taking into account static and dynamic data. This posterior uncertainty can then be propagated to compute probabilistic production forecasts for each scenario, while honoring static and dynamic knowledge of the reservoir. But obtaining posterior uncertainty, as well as propagating it on production forecasts, entails a prohibitive number of reservoir simulations. In this paper, we propose an application of several advanced statistical techniques to perform prediction under uncertainty on a mature field using a reasonable number of simulations. The considered mature field is the PUNQS reservoir model which has been previously used in several comparison studies on uncertainty quantification and history-matching. A workflow based on three steps has been applied. First, a screening and a sensitivity analysis were performed to find the most influential parameters. Then, a probabilistic inversion method was used to reduce uncertainty on the parameters by estimating their posterior uncertainty. Finally, probabilistic predictions are computed by propagating the reduced uncertainty of parameters. In the first step of the workflow, two different sensitivity techniques are discussed and compared. One, more qualitative, based on the Morris method and another, more quantitative, based on Sobol' indices. In the second step, a probabilistic history-matching procedure is applied to reduce the uncertainty. It is based on both a non parametric response surface approach which uses Gaussian process modeling and an adaptive design strategy. In the final step of the workflow, parametric response surfaces are used to approximate the reservoir production forecasts and obtain their probabilistic distribution by propagating the remaining posterior uncertainty of input parameters.