The water mixing experiment in the Generic Mixing Experiment (GEMIX) facility performed at the Paul Scherrer Institute is used as a benchmark case to investigate the influence of the main uncertain parameters on the turbulent mixing under isokinetic flow conditions. The benchmark experiment features two horizontal water streams with the same inlet velocity that merge together to form a mixing flow inside the larger horizontal square channel. The turbulence intensity and the velocity profile at the inlet were used as the main uncertain input parameters. The selected set of computational fluid dynamics (CFD) simulations based on different combinations of values for uncertain parameters has been performed with the code NEPTUNE_CFD that solves the Reynolds Averaged Navier Stokes (RANS) equations with the k-ε turbulence model. To investigate the influence of the uncertain parameters over a wide range of values, the surrogate model called optimal statistical estimator (OSE) was used to generate the response surface of the results. It has been demonstrated that the OSE method can be successfully applied to build the response surface from a limited set of simulation points. For the two-parameter problem of the current study, only a few CFD simulation points are found sufficient to construct the quality response surface.