This proposal aims to develop a new model-based strategy for statistical problems in astronomy involving complex computer models. It embeds computer models into multilevel models in order to explicitly account for complexities in both astronomical sources and in new high-tech telescopes with the aim illuminating the underlying physical processes. Specific methods will be developed to account for calibration uncertainty in X-ray detectors. This involves emulating a computer model for the calibration product and embedding it into a larger model for the detector and the astronomical source. The result will be a dramatic improvement in the assessed uncertainty in fitted parameters, a reduction in false positives and false negatives, and improved robustness of meta-analyses of populations of sources. Methods will also be developed for fitting stellar evolution models. This involves linking multiple computer models via parametric bridges and embedding them into a statistical likelihood. The increased precision of fitted stellar parameters will enable astronomers to identify stellar subpopulations, to study now hidden aspects of Galactic evolution, and to test and refine the physics underlying the stellar evolution models. A final set of new models will better link supernova light curve data with cosmological parameters, thus helping to unlock the secrets of the formation and evolution of the Universe. Since model misspecification can have a serious adverse affect on scientific findings, especially with such complex models, a suite of new model checking and selection techniques will be studied. With his substantial experience developing state-of-the-art scientific computation, advanced methods for statistical inference, and careful model checking procedures, especially in astronomy, van Dyk is ideally suited to carry out this project. The research will be conducted with astronomers in van Dyk's established collaborations and in a new research group at Imperial.