General Bayesian L2 calibration of mathematical models

A mathematical model is a function taking certain arguments and returning a theoretical prediction of a feature of a physical system. The arguments to the mathematical model can be split into two groups; (a) controllable variables of the system; and (b) calibration parameters: unknown characteristics of the physical system that cannot be controlled or directly measured. Of interest is the estimation of the calibration parameter using physical observations. Since the mathematical model will be an inexact representation of the physical system: the aim is to estimate values for the calibration parameters to make the mathematical model ``close" to the physical system. Closeness is defined as the squared $L^2$ norm of the difference between the mathematical model and the physical system. Different Bayesian and general Bayesian methods are introduced, developed and compared for this task.