Reasoning about Uncertainty

Dual properties of the relative belief of singletons

by Fabio Cuzzolin

A study of Bayesian approximations of belief functions in the probability simplex

by Fabio Cuzzolin

"L'incertitude comme menace"

by Claude-Olivier Doron

Draft to be published in Deprins, D. (ed.), Parier sur l'incertitude, Bruxelles, Bruylant, 2012

Through an analysis focusing on penal policies and how they deal with "uncertainty", this article wants to... more Through an analysis focusing on penal policies and how they deal with "uncertainty", this article wants to distinguish between different ways of perceiving and governing uncertainty, what we call different "rationalities" dealing with uncertainty.

Uncertainty and International law

by Oliver Kessler

HEİDEGGER'İN KİRACISI

by berkay dibek

Convex imprecise previsions

by Renato Pelessoni

Co-authored with Paolo Vicig. Published in Reliable Computing, 9 (6), 465-485, 2003.

In this paper centered convex previsions are introduced as a special class of imprecise previsions, showing that they... more In this paper centered convex previsions are introduced as a special class of imprecise previsions, showing that they retain or generalise most of the relevant properties of coherent imprecise previsions but are not necessarily positively homogeneous. The broader class of convex imprecise previsions is also studied and its fundamental properties are demonstrated, introducing in particular a notion of convex natural extension which parallels that of natural extension but has a larger domain of applicability. These concepts appear to have potentially many applications. In this paper they are applied to risk measurement, leading to a general definition of convex risk measure which corresponds, when its domain is a linear space, to the one recently introduced in risk measurement literature.

Convex imprecise previsions: basic issues and applications

by Renato Pelessoni

Co-authored with Paolo Vicig. Published in the Proceedings of the Third International Symposium on Imprecise Probabilities and Their Application, Lugano, Switzerland, pp. 423 - 436, 2003

In this paper we study two classes of imprecise previsions, which we termed convex and centered convex previsions, in... more In this paper we study two classes of imprecise previsions, which we termed convex and centered convex previsions, in the framework of Walley's theory of imprecise previsions. We show that convex previsions are related with a concept of convex natural estension, which is useful in correcting a large class of inconsistent imprecise probability assessments. This class is characterised by a condition of avoiding unbounded sure loss. Convexity further provides a conceptual framework for some uncertainty models and devices, like unnormalised supremum preserving functions. Centered convex previsions are intermediate between coherent previsions and previsions avoiding
sure loss, and their not requiring positive homogeneity is a relevant feature for potential applications. Finally, we show how these concepts can be applied in (nancial) risk measurement.

The Pari-Mutuel Model

by Renato Pelessoni

Co-authored with Paolo Vicig and Marco Zaffalon, published in Proceedings of the Sixth International Symposium on Imprecise Probabilities: Theory and Applications (ISIPTA '09), pp. 347 - 356.

We explore generalizations of the pari-mutuel model (PMM), a formalization of an intuitive way of assessing an upper... more We explore generalizations of the pari-mutuel model (PMM), a formalization of an intuitive way of assessing an upper probability from a precise one. We discuss a naive extension of the PMM considered in insurance and generalize the natural extension of the PMM introduced by P. Walley and other related formulae. The results are subsequently given a risk measurement interpretation: in particular it is shown that a known risk measure, Tail Value at Risk (TVaR), is derived from the PMM, and a coherent risk measure more general than TVaR from its imprecise version. We analyze further the conditions for coherence of a related risk measure, Conditional Tail Expectation. Explicit formulae for conditioning the PMM and conditions for dilation or imprecision increase are also supplied and discussed.

Generalised Dutch Risk Measures

by Renato Pelessoni

Extended abstract co-authored with Paolo Vicig. Published in the Proceedings of the XXXII Amases Conference, Trento, 2008

Some bounds for conditional lower previsions

by Renato Pelessoni

Co-authored with Paolo Vicig. Published in the Proceedings of the Fifth International Symposium on Imprecise Probability: Theories and Applications, Prague, Czech Republic, 2007, pp. 337-346.

In this paper we consider some bounds for lower previsions that are either coherent or centered convex. As for... more In this paper we consider some bounds for lower previsions that are either coherent or centered convex. As for coherent conditional previsions, we adopt a structure-free version of Williams’ coherence, which we compare with Williams’ original version and with other coherence concepts. We then focus on bounds concerning the classical product and Bayes’ rules. After discussing some implications of product rule bounds, we generalise a well-known lower bound, which is a (weak) version for coherent lower probabilities of Bayes’ theorem, to the case of (centered) convex previsions. We obtain a family of bounds and show that one of them is undominated in all cases.

Envelope theorems and dilation with convex conditional previsions

by Renato Pelessoni

Co-authored with Paolo Vicig. Published in the Proceedings of the Fourth International Symposium on Imprecise Probabilities and Their Applications, Pittsburgh, pp. 266 - 275, 2005.

This paper focuses on establishing envelope theorems for convex conditional lower previsions, a recently investigated... more This paper focuses on establishing envelope theorems for convex conditional lower previsions, a recently investigated class of imprecise previsions larger than coherent imprecise conditional previsions. It is in particular discussed how the various theorems can be employed in assessing convex previsions. We also consider the problem of dilation for these kinds of imprecise previsions, and point out the role of convex previsions in measuring conditional risks.

Coherent risk measures and upper previsions

by Renato Pelessoni

Co-authored with Paolo Vicig, published in Proceedings of ISIPTA01, Ithaca, NY, USA, Shaker Publishing BV, 307-315, 2001.

In this paper coherent risk measures and other currently used risk measures, notably Value-at-Risk (VaR), are studied... more In this paper coherent risk measures and other currently used risk measures, notably Value-at-Risk (VaR), are studied from the perspective of the theory of coherent imprecise previsions. We introduce the notion of coherent risk measure defined on an arbitrary set of risks, showing that it can be considered a special case of coherent upper prevision. We also prove that our definition generalizes the notion of coherence for risk measures defined on a linear space of random numbers, given in literature. We also show that Value-at-Risk does not necessarily satisfy a weaker notion of coherence called ‘avoiding sure loss’ (ASL), and discuss both sufficient conditions for VaR to avoid sure loss and ways of modifying VaR into a coherent risk measure.

Roger White's argument against imprecise credences

by Dylan Dodd

Forthcoming in the British Journal for the Philosophy of Science

According to the Imprecise Credence Framework (ICF), a rational
believer's doxastic state should be modeled by a... more According to the Imprecise Credence Framework (ICF), a rational
believer's doxastic state should be modeled by a set of probability functions rather than a single probability function, namely the set of probability functions allowed by the evidence (Joyce [2005]). Roger White ([2010]) has recently given an arresting argument against the ICF, which has garnered a number of responses. In this paper, I attempt to cast doubt on his argument. First, I point out that it's not an argument against the ICF per se, but an argument for the Principle of Indifference. Second, I present an argument that's analogous to White's. I argue that if White's premises are true, the premises of this
argument are too. But the premises of my argument entail something obviously false. Therefore, White's premises must not all be true.

Reasoning in teaching and misleading situations

by Russell Warner

Warner, R., Stoess, T. & Shafto, P. (2011). Reasoning in teaching and misleading situations. In L. Carlson, C. Hölscher, & T. Shipley (Eds.), Proceedings of the 33rd Annual Conference of the Cognitive Science Society (pp. 1430-1435). Boston, MA: Cognitive Science Society.

Much of human inference occurs in social situations. While in many cases, people cooperate, as in teaching settings,... more Much of human inference occurs in social situations. While in many cases, people cooperate, as in teaching settings, people can misdirect others in order to protect their own interests. (Shafto et al, 2008) formalized teaching and learning from teachers as Bayesian inference, in which learners use knowledge about the teacher's intent to facilitate inference. This same model provides a basis for exploring reasoning about misleading. We present two new experiments comparing reasoning about teaching and misleading. In both experiments, participants play the role of informant (teacher/misleader) or learner. Our model predicts and our results show that people's behavior differs in teaching and misleading conditions, both when intentions are explicitly known as well as when they are not. Further, the model provides close fits to informants' and learners' behavior.

Moral Reasoning Under Uncertainty

by The Anh Han

co-authored with A. Saptawijaya and L. M. Pereira.
In Proceedings of the 18th International Conference on Logic for Programming Artificial Intelligence and Reasoning (LPAR 2012), Springer LNAI, 2012

We present a Logic Programming framework for moral reasoning under uncertainty. It is enacted by a coherent... more We present a Logic Programming framework for moral reasoning under uncertainty. It is enacted by a coherent combination of our two previously implemented systems, Evolution Prospection for decision making, and P-log for probabilistic inference. It allows computing available moral judgments via distinct kinds of prior and post preferences. In introducing various aspects of uncertainty into cases of classical trolley problem moral dilemmas, we show how they may appropriately influence moral judgments, allowing decision makers to opt for different choices, and for these to be externally appraised, even when subject to incomplete evidence, as in courts.

Happiness and Uncertainty

by Christopher Groves

Fukushima : limites anthropologiques à la complexité et risque d'effondrement sociétal

by François Diaz Maurin

Dossier N°12 : Fukushima, fin de l’Anthropocène ?
Entropia - ISSN 1954-2437 (http://www.entropia-la-revue.org/)
Printemps 2012 (à paraître)

Aujourd'hui, à l'ère de l'Anthropocène, le recours à l'énergie nucléaire pour la production d'électricité est de loin... more Aujourd'hui, à l'ère de l'Anthropocène, le recours à l'énergie nucléaire pour la production d'électricité est de loin le système énergétique le plus complexe jamais entrepris par l'homme. Or, les accidents de Fukushima ont démontré l'incapacité de l'humanité à contrôler ce système complexe.

Approaches to displaying information to assist decisions under uncertainty

by Melanie Kreye

Yee Mey Goh, Linda B. Newnes

In the early product design stage, considering the Through Life Cost and uncertainty are important. However, the... more In the early product design stage, considering the Through Life Cost and uncertainty are important. However, the information given to the decision maker is often limited, resulting in a large level of subjectivity. This paper introduces experimental research exploring different information displays and their subjective interpretation by cost forecasters within the defence and aerospace sector. Three different kinds of information display and different levels of detail of contextual information were tested, showing that they impact the decision making process and subjective interpretation.

The reasoning behind informal statistical inference

by Arthur Bakker

Makar, K., Bakker, A., & Ben-Zvi, D. (2011). The reasoning behind informal statistical inference. Mathematical Thinking and Learning, 13, 152-173.

Informal statistical inference (ISI) has been a frequent focus of recent research in statistics education. Considering... more Informal statistical inference (ISI) has been a frequent focus of recent research in statistics education. Considering the role that context plays in developing ISI calls into question the need to be more explicit about the reasoning that underpins ISI. This paper uses educational literature on informal statistical inference and philosophical literature on inference to argue that in order for students to generate informal statistical inferences, there are a number of interrelated key elements that are needed to support their informal inferential reasoning. In particular, we claim that ISI is nurtured by statistical knowledge, knowledge about the problem context, and useful norms and habits developed over time, and is supported by an inquiry-based environment (tasks, tools, scaffolds). We adopt Peirce's and Dewey's view that inquiry is a sense-making process driven by doubt and belief, leading to inferences and explanations. To illustrate the roles that these elements play in supporting students to generate informal statistical inferences, we provide an analysis of three sixth-graders' (aged 12) informal inferential reasoning—the reasoning processes leading to their informal statistical inferences

Efficient Epistemic Reasoning in Partially Observable Dynamic Domains Using Hidden Causal Dependencies

by Theodore Patkos