This paper discusses verification and optimization of complex systems with respect to a set of specifications under stochastic parameter variations. We introduce a simulation-based statistically sound model inference approach that considers systems whose responses depend on a few design parameters and many stochastic parameters. The technique iteratively searches over the space of design parameters by alternating between verification and optimization phases. The verification phase uses statistical model checking to check if the model using the current design parameters satisfies the specifications. Failing this, we seek new values of the design parameters for which statistical verification could potentially succeed. This is achieved through repeated simulations for various values of the design and stochastic parameters, and quantile regression to construct a model that predicts the spread of the responses as a function of the design parameters. The resulting model is used to select a new set of values for the design parameters. We evaluate this approach over several benchmark examples. In each case, the performance is improved significantly compared to the nominal design.