ISIPTA'07: Proceedings of the Fifth International Symposium on Imprecise Probability: Theories and Applications

B

Computational Determination of Coherence of Financial Risk Measure as a Lower Prevision of Imprecise Probability

This study is about developing some further ideas in imprecise probability models of financial risk measures. A financial risk measure has been interpreted as an upper prevision of imprecise probability, which through the conjugacy relationship can be seen as a lower prevision. The risk measures selected in the study are value-at-risk (VaR) and conditional value-at-risk (CVaR). The notion of coherence of risk measures is explained. Stocks that are traded in the financial markets (the risky assets) are seen as the gambles. The study makes a determination through computation from actual assets data whether the risk measure assessments of gambles (assets) are coherent as an imprecise probability. It is observed that coherence of assessments depends on the asset's returns distribution characteristic

Formal explorations in collective and individual rationality

This thesis addresses several questions regarding what rational agents ought to believe and how they ought to act. In the first part I begin by discussing how scientists contemplating several mutually exclusive theories, models or hypotheses can reach a rational decision regarding which one to endorse. In response to a recent argument that they cannot, I employ the tools of social choice theory to offer a ‘possibility result’ for rational theory choice. Then I utilize the tools of judgment aggregation to investigate how scientists from across fields can pool their expertise together. I identify an impossibility result threatening such a procedure and prove a possibility result which requires that some scientists sometimes waive their expertise over some propositions. In the second part I first discuss the existing justifications for a restricted principle of indifference that mandates that two agents whose experiences are subjectively indistinguishable should be indifferent with respect to their identities. I argue that all existing justifications rely on the same mistaken reasoning behind the ‘staying’ strategy in the Monty Hall problem. Secondly, I show this mistake is more widespread and I identify it in arguments purporting to show the failure of two reflection-like principles. In the third part I look at a recent argument that fair policy makers face a dilemma when trying to correct a biased distributive process. I show the dilemma only holds if the correction has to happen in one-shot. Finally, I look at how we ought to design public restrooms so that we reduce the discrimination faced by minority groups. I make the case for opening our public restrooms to all genders

Scientific uncertainty and decision making

It is important to have an adequate model of uncertainty, since decisions must be made before the uncertainty can be resolved. For instance, flood defenses must be designed before we know the future distribution of flood events. It is standardly assumed that probability theory offers the best model of uncertain information. I think there are reasons to be sceptical of this claim. I criticise some arguments for the claim that probability theory is the only adequate model of uncertainty. In particular I critique Dutch book arguments, representation theorems, and accuracy based arguments. Then I put forward my preferred model: imprecise probabilities. These are sets of probability measures. I offer several motivations for this model of uncertain belief, and suggest a number of interpretations of the framework. I also defend the model against some criticisms, including the so-called problem of dilation. I apply this framework to decision problems in the abstract. I discuss some decision rules from the literature including Levi’s E-admissibility and the more permissive rule favoured by Walley, among others. I then point towards some applications to climate decisions. My conclusions are largely negative: decision making under such severe uncertainty is inevitably difficult. I finish with a case study of scientific uncertainty. Climate modellers attempt to offer probabilistic forecasts of future climate change. There is reason to be sceptical that the model probabilities offered really do reflect the chances of future climate change, at least at regional scales and long lead times. Indeed, scientific uncertainty is multi-dimensional, and difficult to quantify. I argue that probability theory is not an adequate representation of the kinds of severe uncertainty that arise in some areas in science. I claim that this requires that we look for a better framework for modelling uncertaint

Advanced system engineering approaches to dynamic modelling of human factors and system safety in sociotechnical systems

Sociotechnical systems (STSs) indicate complex operational processes composed of interactive and dependent social elements, organizational and human activities. This research work seeks to fill some important knowledge gaps in system safety performance and human factors analysis using in STSs. First, an in-depth critical analysis is conducted to explore state-of-the-art findings, needs, gaps, key challenges, and research opportunities in human reliability and factors analysis (HR&FA). Accordingly, a risk model is developed to capture the dynamic nature of different systems failures and integrated them into system safety barriers under uncertainty as per Safety-I paradigm. This is followed by proposing a novel dynamic human-factor risk model tailored for assessing system safety in STSs based on Safety-II concepts. This work is extended to further explore system safety using Performance Shaping Factors (PSFs) by proposing a systematic approach to identify PSFs and quantify their importance level and influence on the performance of sociotechnical systems’ functions. Finally, a systematic review is conducted to provide a holistic profile of HR&FA in complex STSs with a deep focus on revealing the contribution of artificial intelligence and expert systems over HR&FA in complex systems. The findings reveal that proposed models can effectively address critical challenges associated with system safety and human factors quantification. It also trues about uncertainty characterization using the proposed models. Furthermore, the proposed advanced probabilistic model can better model evolving dependencies among system safety performance factors. It revealed the critical safety investment factors among different sociotechnical elements and contributing factors. This helps to effectively allocate safety countermeasures to improve resilience and system safety performance. This research work would help better understand, analyze, and improve the system safety and human factors performance in complex sociotechnical systems

A personalist doctrine of providence: Karl Barth's Church Dogmatics III.3 in conversation with philosophical theology

In this thesis I present a critical explication of Barth’s doctrine of providence in Church Dogmatics III.3. I argue that Karl Barth’s doctrine of providence developed throughout CD III.3 represents a ‘personalist’ revision of Reformed orthodoxy which can only be understood through his ad hoc use of philosophical resources. I claim that critics and supporters alike have missed the depth of Barth’s revision of Reformed providence by failing to perceive his ad hoc use of contemporaneous philosophical tools of the personal. Barth’s doctrine of providence remains theology proper, and not philosophy, but cannot be understood without philosophy. By setting Barth in conversation with three philosophical theologians, Vincent Brümmer, John Macmurray and Austin Farrer, I attempt to show how far Barth is from pre-modern understandings in his articulation of the doctrine of providence. These conversations equip the reader to discern continuities and discontinuities of Barth’s thought with 20th century personal, relational philosophy, thereby making sense of many of Barth’s counterintuitive claims. For Barth, human life is the continual double-agency of human self-determination and divine determination. This life in covenant before God (coram Deo) constitutes the Godgiven opportunity of human personhood. Seen in dialogue with personalist philosophical thinkers, Barth’s doctrine of providence overcomes problematic aspects of traditional Reformed views and grants limited time and space for personal development. Providence sheds light on Barth’s ‘eternalizing’ eschatology in that election establishes the objective reality of salvation for all creatures, while providence explicates God’s active lordship in the human’s self-determination of personal identity in history (the subjective formation of the person who is objectively saved). Election describes God’s salvific work on behalf of creation solely in the work of Jesus Christ. Providence determines the identity of those creatures in relation with the personal God. The conversations I propose with philosophical theologians enable the reader to discern a greater philosophical coherence in Barth’s doctrine of providence. Through contrast with the philosophical theologians, Barth’s christocentric and Trinitarian articulation gains clarity and significance. Building on these philosophical comparisons, I attempt to assess Barth’s elaborations on entrenched debates concerning history as determined by divine action, human freedom under divine providence, and the problem of evil in world-occurrence. I argue that Barth’s ‘personalist’ post-Enlightenment providence as seen in the whole of III.3 points to absolute confidence in God’s determination of all world-occurrence, limited human autonomy of action under God’s universal providence, and an explication of evil that strengthens the Christian in the face of suffering and injustice

The Material Theory of Induction

The fundamental burden of a theory of inductive inference is to determine which are the good inductive inferences or relations of inductive support and why it is that they are so. The traditional approach is modeled on that taken in accounts of deductive inference. It seeks universally applicable schemas or rules or a single formal device, such as the probability calculus. After millennia of halting efforts, none of these approaches has been unequivocally successful and debates between approaches persist. The Material Theory of Induction identifies the source of these enduring problems in the assumption taken at the outset: that inductive inference can be accommodated by a single formal account with universal applicability. Instead, it argues that that there is no single, universally applicable formal account. Rather, each domain has an inductive logic native to it.The content of that logic and where it can be applied are determined by the facts prevailing in that domain. Paying close attention to how inductive inference is conducted in science and copiously illustrated with real-world examples, The Material Theory of Induction will initiate a new tradition in the analysis of inductive inference