The role of mechanistic models in Bayesian inference

I'll outline the role of mechanistic models, or simulators, in defining priors in a Bayesian inference setting. In particular I will focus on two main cases: 1) where process based understanding of the system allows us to construct a stochastic simulator for the system - which translates to inference in stochastic processes; 2) where an existing (typically) deterministic mechanistic model exists - which we can then emulate and treat 'correctly' in a Bayesian manner. I will pay special attention to the relation between the simulator and reality, since it is reality that typically is sampled to generate the observations used for inference in the model. I will outline ideas from emulation, and show the challenges I think remain to be solved. This is joint work with lots of people: Alexis Boukouvalas, Yuan Shen, Michael Vrettas, Manfred Opper and many others in the MUCM project.