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Title: General Bayesian design of experiments for calibration of mathematical models Authors:  Antony Overstall - University of Southampton (United Kingdom) [presenting]
Abstract: A mathematical model is a representation of a physical system often derived from scientific theory. It is considered to be a function of certain arguments, returning a theoretical prediction of a feature (or features) of the physical system. The arguments are assumed to belong to two groups: (a) controllable inputs, and (b) unknown calibration parameters. Observations of the physical system, for certain controllable inputs, can be used to attribute values to the calibration parameters, a process known as calibration. The values given to the calibration parameters should, in some senses, result in the mathematical model being ``close'' to the physical system. This goal implicitly recognises that there do not exist values of the calibration parameters such that the mathematical model is equal to the physical system for all values of the controllable inputs. The ``distance'' between the mathematical model and the physical system can be represented by a loss function, which, in turn, defines a general Bayesian posterior distribution. The aim is to design a calibration experiment, i.e., the choice of controllable inputs at which to observe the physical system to reduce uncertainty exhibited by the general Bayesian posterior under a chosen loss function.