A Bayes Linear Approach to Making Inferences from X-rays

X-ray images are often used to make inferences about physical phenomena and the entities about which inferences are made are complex. The Bayes linear approach is a generalisation of subjective Bayesian analysis suited to uncertainty quantification for complex systems. Therefore, Bayes linear is an appropriate tool for making inferences from X-ray images. In this thesis, I will propose methodology for making inferences about quantities, which may be organised as multivariate random fields. A number of problems will be addressed: anomaly detection, emulation, inverse problem solving and transferable databases. Anomaly detection is deciding whether a new observation belongs to the same population as a reference population, emulation is the task of building a statistical model of a complex computer model, inverse problem solving is the task of making inferences about system values, given an observation of system behaviour and transferable databases is the task of using a data-set created using a simulator to make inferences about physical phenomena. The methods we use to address these problems will be exemplified using applications from the X-ray industry. Anomaly detection will be used to identify plastic contaminants in chocolate bars, emulation will be used to efficiently predict the scatter present in an X-ray image, inverse problem solving will be used to infer an entity's composition from an X-ray image and transferable databases will be used to improve image quality and return diagnostic measures from clinical X-ray images. The Bayes linear approach to making inferences from an X-ray image enables improvements over the state-of-the-art approaches to high impact problems.