Proposal summary (half page, possibly copy/paste abstract from the administrative form A1)Observations of the Cosmic Microwave Background (CMB) allow us to see 98% of the way to the big bang, back to a time when the Universe was only a few hundred thousand years old. Other forthcoming data will probe the more local universe in great detail. To test different possible universe models we need accurate theoretical predictions for this data in each model, and new sampling methods to solve the inference problem.CMB data is most powerful if combined with information from other sources, allowing us to test many possible models of the universes and constrain cosmological parameters. As more models and parameters can be constrained, and higher precision means that more small uncertain corrections need to be consistently modelled, the problem of inference becomes challenging. I propose to develop ground-breaking new sampling methods for testing models with many parameters. To do this I will find novel sampling techniques, make efficient use of qualitatively different properties of different parameters, and develop a new parallelized sampling code that can be run on-demand in the cloud, leveraging the power of potentially vast and cheap cloud computing facilities and freeing up dedicated supercomputers for the problems where they are really needed.In addition my team will develop new accurate theoretical predictions for confrontation with data, including analysis of new non-linear processes that will be a major source of confusion for dark energy and early universe studies, as well as correlations between different data sets.I am applying for 70% of my time and two ERC postdocs to tackle these challenges.