Probabilistic formulations for transferring inferences from mathematical models to physical systems

We outline a probabilistic framework for linking mathematical models to the physical systems that they represent, taking account of all sources of uncertainty including model and simulator imperfections. This framework is a necessary precondition for making probabilistic statements about the system on the basis of evaluations of computer simulators. We distinguish simulators according to their quality and the nature of their inputs. Where necessary, we introduce further hypothetical simulators as modelling constructs to account for imperfections in the available simulators and to unify the available simulators with the underlying system.