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 firstname.lastname@example.org. Suggestions for prominent speakers outside the IP community, whose work is nevertheless related to IP, are especially welcome.
On the Interplay of Optimal Transport and Distributionally Robust OptimizationDaniel Kuhn 12 December 2023, 15:00 CET
Zoom link: https://utc-fr.zoom.us/j/82027992604
Optimal Transport (OT) seeks the most efficient way to morph one probability distribution into another one, and Distributionally Robust Optimization (DRO) studies worst-case risk minimization problems under distributional ambiguity. It is well known that OT gives rise to a rich class of data-driven DRO models, where the decision-maker plays a zero-sum game against nature who can adversely reshape the empirical distribution of the uncertain problem parameters within a prescribed transportation budget. Even though generic OT problems are computationally hard, the Nash strategies of the decision-maker and nature in OT-based DRO problems can often be computed efficiently. In this talk we will uncover deep connections between robustification and regularization, and we will disclose striking properties of nature’s Nash strategy, which implicitly constructs an adversarial training dataset. We will also show that OT-based DRO offers a principled approach to deal with distribution shifts and heterogeneous data sources, and we will highlight new applications of OT-based DRO in machine learning, statistics, risk management and control. Finally, we will argue that, while OT is useful for DRO, ideas from DRO can also help us to solve challenging OT problems.
Falsification, Fisher's underworld of probability, and balancing behavioral & statistical reliabilityRyan Martin 18 October 2023, 15:00 CEST
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Statisticians develop methods to assist in building probability statements that will be used to make inference on relevant unknowns. Popper argued that probability statements themselves can’t be falsified, but what about the statistical methods that use data to generate them? Science today is largely empirical, so if statistical methods’ conversion of data into scientific judgments can’t be scrutinized, then it’s not fair to expect society to “trust the science.”
Fisher’s underworld of probability concerns layers below the textbook surface level, where knowledge is vague and imprecise. Roughly, suppose that an agent quantifies his uncertainty about a relevant unknown via (imprecise) probability statements, which defines his betting odds. Now suppose that a second agent, who may not have her own probability statements about the relevant unknown, believes that the first agent’s assessments are wrong and can formulate odds at which she’d bet against the first agent’s wagers. If the second agent wins in these side-bets, then she reveals a shortcoming in the first agent’s assessments. I claim that the statistical method and “society” above are like the first and second agents here, respectively, and that scrutiny of a statistical method proceeds by giving “society” an opportunity to bet against its claims.
In this talk, I’ll carry out this scrutiny formally/mathematically and present some key take-aways. No surprise, a statistical method that’s falsification-proof in this sense is the behaviorally most reliable and conservative generalized Bayes rule. More surprising, however, is that a necessary condition for being falsification-proof is a statistical reliability property – called validity – that I’ve been advocating for recently. It follows, then, from the false confidence theorem that statistical methods quantifying uncertainty via precise probabilities can typically be falsified in this sense. More generally, since validity also implies certain behavioral reliability properties and needn’t be overly conservative, my new possibilistic inference framework (which I’ll describe and illustrate) is a promising way to balance the behavioral and statistical reliability properties.
Knightian Uncertainty in Finance and EconomicsFrank Riedel 30 March 2023, 15:00 CET
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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.
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.