This programme of research will develop the new approaches to Bayesian data science that are needed both within the health sciences and more widely. It builds on recent breakthroughs in Monte Carlo integration methods that show great promise for being efficient for large data; and on new paradigms for Bayesian-like updates that are suitable for complex models and which focus modelling effort just on the aspects of these models that are most important. It will address key research challenges in the health sciences -- directly developing new insights and understanding for these.