Confirmation, Decision, and Evidential Probability

Henry Kyburg’s theory of Evidential Probability offers a neglected tool for approaching problems in confirmation theory and decision theory. I use Evidential Probability to examine some persistent problems within these areas of the philosophy of science. Formal tools in general and probability theory in particular have great promise for conceptual analysis in confirmation theory and decision theory, but they face many challenges. In each chapter, I apply Evidential Probability to a specific issue in confirmation theory or decision theory. In Chapter 1, I challenge the notion that Bayesian probability offers the best basis for a probabilistic theory of evidence. In Chapter 2, I criticise the conventional measures of quantities of evidence that use the degree of imprecision of imprecise probabilities. In Chapter 3, I develop an alternative to orthodox utility-maximizing decision theory using Kyburg’s system. In Chapter 4, I confront the orthodox notion that Nelson Goodman’s New Riddle of Induction makes purely formal theories of induction untenable. Finally, in Chapter 5, I defend probabilistic theories of inductive reasoning against John D. Norton’s recent collection of criticisms. My aim is the development of fresh perspectives on classic problems and contemporary debates. I both defend and exemplify a formal approach to the philosophy of science. I argue that Evidential Probability has great potential for clarifying our concepts of evidence and rationality

Specifying nonspecific evidence

In an earlier article [J. Schubert, On nonspecific evidence, Int. J. Intell. Syst. 8(6), 711-725 (1993)] we established within Dempster-Shafer theory a criterion function called the metaconflict function. With this criterion we can partition into subsets a set of several pieces of evidence with propositions that are weakly specified in the sense that it may be uncertain to which event a proposition is referring. Each subset in the partitioning is representing a separate event. The metaconflict function was derived as the plausibility that the partitioning is correct when viewing the conflict in Dempster's rule within each subset as a newly constructed piece of metalevel evidence with a proposition giving support against the entire partitioning. In this article we extend the results of the previous article. We will not only find the most plausible subset for each piece of evidence as was done in the earlier article. In addition we will specify each piece of nonspecific evidence, in the sense that we find to which events the proposition might be referring, by finding the plausibility for every subset that this piece of evidence belong to the subset. In doing this we will automatically receive indication that some evidence might be false. We will then develop a new methodology to exploit these newly specified pieces of evidence in a subsequent reasoning process. This will include methods to discount evidence based on their degree of falsity and on their degree of credibility due to a partial specification of affiliation, as well as a refined method to infer the event of each subset.Comment: 39 pages, 2 figure

Decision-support methodology to assess risk in end-of-life management of complex systems

End-of-life management of complex systems is increasingly important for industry because of growing environmental concerns and associated regulations. In many areas, lack of hindsight and significant statistical information restricts the efficiency of end-of-life management processes and additional expert knowledge is required. In this context and to promote the reuse of secondhand components, a methodology supported by risk assessment tools is proposed. The proposal consists of an approach to combine expert and statistical knowledge to improve risk assessment. The theory of belief functions provides a common framework to facilitate fusion of multisource knowledge, and a directed evidential network is used to compute a measure of the risk level. An additional indicator is proposed to determine the result quality. Finally, the approach is applied to a scenario in aircraft deconstruction. In order to support the scientific contribution, a software prototype has been developed and used to illustrate the processing of directed evidential networks

Evidential uncertainties on rich labels for active learning

Recent research in active learning, and more precisely in uncertainty sampling, has focused on the decomposition of model uncertainty into reducible and irreducible uncertainties. In this paper, we propose to simplify the computational phase and remove the dependence on observations, but more importantly to take into account the uncertainty already present in the labels, \emph{i.e.} the uncertainty of the oracles. Two strategies are proposed, sampling by Klir uncertainty, which addresses the exploration-exploitation problem, and sampling by evidential epistemic uncertainty, which extends the reducible uncertainty to the evidential framework, both using the theory of belief functions

How to Treat Expert Judgment? With certainty it contains uncertainty!

PresentationTo be acceptably safe one must identify the risks one is exposed to. It is uncertain whether the threat really will materialize, but determining the size and probability of the risk is also full of uncertainty. When performing an analysis and preparing for decision making under uncertainty, quite frequently failure rate data, information on consequence severity or on a probability value, yes, even on the possibility an event can or cannot occur is lacking. In those cases, the only way to proceed is to revert to expert judgment. Even in case historical data are available, but one should like to know whether these data still hold in the current situation, an expert can be asked about their reliability. Anyhow, expert elicitation comes with an uncertainty depending on the expert’s reliability, which becomes very visible when two or more experts give different answers or even conflicting ones. This is not a new problem, and very bright minds have thought how to tackle it. But so far, however, the topic has not been given much attention in process safety and risk assessment. The paper has a review character and will present various approaches with detailed explanation and examples