Evaluation of elicitation methods to quantify Bayes linear models

The Bayes linear methodology allows decision makers to express their subjective beliefs and adjust these beliefs as observations are made. It is similar in spirit to probabilistic Bayesian approaches, but differs as it uses expectation as its primitive. While substantial work has been carried out in Bayes linear analysis, both in terms of theory development and application, there is little published material on the elicitation of structured expert judgement to quantify models. This paper investigates different methods that could be used by analysts when creating an elicitation process. The theoretical underpinnings of the elicitation methods developed are explored and an evaluation of their use is presented. This work was motivated by, and is a precursor to, an industrial application of Bayes linear modelling of the reliability of defence systems. An illustrative example demonstrates how the methods can be used in practice

Twin Paradox and the logical foundation of relativity theory

We study the foundation of space-time theory in the framework of first-order logic (FOL). Since the foundation of mathematics has been successfully carried through (via set theory) in FOL, it is not entirely impossible to do the same for space-time theory (or relativity). First we recall a simple and streamlined FOL-axiomatization SpecRel of special relativity from the literature. SpecRel is complete with respect to questions about inertial motion. Then we ask ourselves whether we can prove usual relativistic properties of accelerated motion (e.g., clocks in acceleration) in SpecRel. As it turns out, this is practically equivalent to asking whether SpecRel is strong enough to "handle" (or treat) accelerated observers. We show that there is a mathematical principle called induction (IND) coming from real analysis which needs to be added to SpecRel in order to handle situations involving relativistic acceleration. We present an extended version AccRel of SpecRel which is strong enough to handle accelerated motion, in particular, accelerated observers. Among others, we show that the Twin Paradox becomes provable in AccRel, but it is not provable without IND.Comment: 24 pages, 6 figure

A Survey on Continuous Time Computations

We provide an overview of theories of continuous time computation. These theories allow us to understand both the hardness of questions related to continuous time dynamical systems and the computational power of continuous time analog models. We survey the existing models, summarizing results, and point to relevant references in the literature

Die Bedeutung einer Ausfallbedrohtheit von Versicherungskontrakten - ein Beitrag zur Behavioral Insurance

Kahneman/Tversky 1979 haben das theoretische Konstrukt der Probabilistic Insurance Kontrakte in die Literatur eingeführt. Hiermit werden Versicherungsverträge bezeichnet, deren Erfüllung im Leistungsfalle aufgrund einer möglichen Insolvenz des Versicherungsunternehmens nicht gewährleistet ist. In Ausweitung einer Studie von Wakker/Thaler/Tversky 1997 wird in der vorliegenden Arbeit eine experimentelle Untersuchung durchgeführt, wobei die Zahlungsbereitschaft potentieller Versicherungsnehmer in Abhängigkeit des Ratings des den Versicherungskontrakt anbietenden Unternehmens festgestellt wird. Dabei zeigt sich, daß diese ausfallbedrohte Versicherungsprodukte relativ zu ausfallfreien Verträgen mit erheblichen Prämienabschlägen sanktionieren. Der Preisabschlag nimmt dabei mit sinkender Unternehmensbonität (erhöhter Ausfallgefahr) zu. Die Befragungsergebnisse zeigen zudem das neuartige Phänomen, daß mit zunehmender Ausfallbedrohtheit immer weniger Personen bereit sind, ausfallbedrohte Versicherungsprodukte überhaupt zu akzeptieren. Schließlich werden Schlußfolgerungen für die Steuerung von Versicherungsunternehmen diskutiert