A Bayesian formulation adapted from Kennedy and O'Hagan (2001) and Higdon et al. (2008) is used to give parameter constraints from physical observations and a limited number of simulations. The framework is based on the idea of replacing the simulator by an emulator which can then be used to facilitate computations required for the analysis. In this talk I'll describe the details of this approach and apply it to an example that uses large scale structure of the universe to inform about a subset of the parameters controlling a cosmological model. I'll also explain basics of using Gaussian process models and compare them to an approach that uses the ensemble Kalman filter.