The Society for Imprecise Probabilities:
Theories and Applications

SIPTA Seminars

Are you a curious student that has just started to explore the topic of imprecise probabilities? Or an experienced researcher that would like to keep in touch with the community? Join us at the SIPTA Seminars, an online series of seminars on imprecise probabilities (IP). The seminars are open to anyone interested in IP, and are followed by a Q&A and open discussion. They take place roughly once per month, with a break over the summer. Topics range from foundational IP theories to applications that can benefit from IP approaches.

Details about the individual seminars are available in the list below. Close to the date of the next seminar, a zoom link will be provided there as well, which is freely accessible. If you click it, you will first be taken to a waiting room; please be patient until the organizers let you in. During the talk, questions should be put in the chat, and the audience is expected to mute their microphones. After the talk, there will be time for Q&A and discussion, at which point you can turn on your microphone when you want to contribute. The talk (but not the Q&A and discussion) will be recorded, and will afterwards be made freely available on the SIPTA Youtube channel.

The organisation is taken care of by Sébastien Destercke, Enrique Miranda and Jasper De Bock. If you have questions about the seminars, or suggestions for future speakers, you can get in touch with us at Suggestions for prominent speakers outside the IP community, whose work is nevertheless related to IP, are especially welcome.

Upcoming Seminars

Knightian Uncertainty in Finance and Economics

Frank Riedel 30 March 2023, 15:00 CET

Zoom link:
The talk discusses the foundations of decision making under Knightian uncertainty, i.e. in situations when the relevant probability distributions are unknown, or only partially known. After reviewing the basic concepts and models that have been developed in decision theory on the one hand, and mathematical finance on the other hand, we put special emphasis on markets under uncertainty in so-called identified models where recently some substantial progress has been made.

Past Seminars

Some finitely additive probabilities and decisions

Teddy Seidenfeld 17 February 2023, 15:00 CET

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Imprecise Probability’s roots grow in de Finetti’s fertile foundations of coherent decision making. A continuing theme in de Finetti’s work is that coherence does not require expectations to be countably additive. In this presentation (involving joint work with Jay Kadane, Mark Schervish, and Rafael Stern) I review two contexts: the first one about probabilities for (logical) Boolean algebras; the second one about admissibility in statistical decision theory, that require merely finitely additive (not countably additive) expectations. The common perspective for viewing the two contexts is through the requirement of countably additivity – as presented in Kolmogorov’s theory – as a continuity principle. In each of the two contexts such continuity is precluded, but in very different ways.

Engineering and IP: what's going on?

Alice Cicirello, Matthias Faes & Edoardo Pattelli 13 January 2023, 15:00 CET

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Engineers design components, structures and systems and plan activities to extend their service lives despite a limited understanding of the underlying physics and/or the availability of sufficient informative data. A big challenge is to deal with unknown and uncontrollable variables such as changes on the environmental conditions, deliberated threats, change of intended use, etc. As a result of this, large safety factors are usually adopted in order to mitigate the use of approximate methods and deal with uncertainty. Often the methods for dealing with uncertainty assume a complete knowledge of the underlying stochastic process. This wide availability of information is however rarely the case in practice. Although imprecise probability offers the tools to cope with lack of knowledge and data, it is not largely adopted in practice. One of the main reasons is the lack of accessible and efficient tools, both analytical and numerical, for uncertainty quantification. On top, there exists still a lack of awareness of the potential capabilities of imprecise probability theory and its applications. In this seminar, we are presenting the challenges in the application of imprecise probability to practical engineering problems These challenges have been the driver for several novel algorithms and approaches that are going to be presented.

Dealing with Uncertain Arguments in Artificial Intelligence

Fabio Cozman 29 November 2022, 15:00 CET

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Argumentation techniques have received significant attention in Artificial Intelligence, particularly since 1995, when Dung proposed his "argumentation frameworks" and showed that they unify many branches of knowledge representation. Argumentation frameworks that deal with uncertainty have been explored since then; often, these frameworks rely on imprecise or indeterminate probabilities. Indeed, probabilistic argumentation frameworks may be one of the most promising applications of imprecise probabilities in Artificial Intelligence. This talk will review the main ideas behind argumentation frameworks and how they are often connected with imprecise probabilities.

Coalitional game theory vs Imprecise probabilities: Two sides of the same coin ... or not?

Ignacio Montes 21 October 2022, 15:00 CEST

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Lower probabilities, defined as normalised and monotone set functions, constitute one of the basic models within Imprecise Probability theory. One of their interpretations allows building a bridge with coalitional game theory: the possibility space is regarded as a set of players who must share a reward, events represent coalitions of players who collaborate in order to obtain a greater reward, and the lower probability of a coalition represents the minimum reward that this collaboration can guarantee. This correspondence makes lower probabilities and coalitional games formally equivalent, being the notation, terminology and interpretation the only difference. As an example, coherent lower probabilities are the same as exact games, the credal set of the lower probability is referred to as the core of the game,... In this presentation I dig into this connection, paying special attention to game solutions and their interpretation as centroids of the credal set. In addition, I show that if we move to the more general setting of lower previsions, it is possible to represent information about the coalitions and their rewards that cannot be captured by the standard coalitional game theory. This shows that lower previsions constitute a more general framework than the classical theory of coalitional games.

E is the new P

Peter Grünwald 29 September 2022, 15:00 CEST

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We develop a representation of a decision maker's uncertainty based on e-values, a recently proposed alternative to the p-value. Like the Bayesian posterior, this e-posterior allows for making predictions against arbitrary loss functions that do not have to be specified ex ante. Unlike the Bayesian posterior, it provides risk bounds that have frequentist validity irrespective of prior adequacy: if the e-collection (which plays a role analogous to the Bayesian prior) is chosen badly, bounds get loose rather than wrong. As a consequence, e-posterior minimax decision rules are safer than Bayesian ones. The resulting quasi-conditional paradigm addresses foundational issues in statistical inference. If the losses under consideration have a special property which we call Condition Zero, risk bounds based on the standard e-posterior are equivalent to risk bounds based on a `capped' version of it. We conjecture that this capped version can be interpreted in terms of possibility measures and Martin-Liu inferential models.

Imprecise probabilities in modern data science: challenges and opportunities

Ruobin Gong 29 June 2022, 15:00 CEST

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Imprecise probabilities (IP) capture structural uncertainty intrinsic to statistical models. They offer a richer vocabulary with which the modeler may articulate specifications without concocting unwarranted assumptions. While IP promises a principled approach to data-driven decision making, its use in practice has so far been limited. Two challenges to its popularization are 1) IP reasoning may defy the intuition we derive from precise probability models, and 2) IP models may be difficult to compute. On the other hand, recent developments in formal privacy present a unique opportunity for IP to contribute to responsible data dissemination. Case in point is differential privacy (DP), a cryptographically motivated framework endorsed by corporations and official statistical agencies including the U.S. Census Bureau. I discuss how IP offers the correct language for DP, both descriptive and inferential, particularly when the privacy mechanism lacks transparency. These challenges and opportunities highlight the urgency to adapt IP research to meet the demands of modern data science.

Imprecision, not as a problem, but as part of the solution

Gert de Cooman 30 May 2022, 15:00 CEST

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Imprecision in probability theory is often considered to be unfortunate, something to be tolerated, and then only if there is no other way out. In this talk, I will argue that imprecision also has strongly positive sides, and that it can allow us to look at, approach and deal with existing problems in novel ways. I will provide a number of examples to corroborate for this thesis, based on my research experience in a number of fields: inference and decision making, stochastic processes, algorithmic randomness, game-theoretic probability, functional analysis, ...