# 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 seminars@sipta.org. Suggestions for prominent speakers outside the IP community, whose work is nevertheless related to IP, are especially welcome.

## Upcoming seminars

### TBA

Barbara Vantaggi 26 March 2024, 15:00 CETThe Zoom link will appear here close to the start of the seminar

## Past seminars

### Mixing time and uncertainty. A tale of superpositions

Rafael Peñaloza Nyssen 14 February 2024Watch on YouTube

### Fundamentally finitary foundations for probability and bounded probability

Matthias Troffaes 31 January 2024Watch on YouTube

Bounded probability uses sets of probability measures, specified through bounds on expectations, to represent states of severe uncertainty. This approach has been successfully applied to a wide range of fields where risk under severe uncertainty is a concern.

Following Walley’s work from the 90’s, the canonical interpretation of these bounds has been through betting. However, in high-risk situations where the assessor themselves is at risk, various authors have argued that the betting interpretation of probability, and therefore also of lower previsions, cannot be applied. For this reason, in 2006, Lindley suggested an alternative interpretation of probability, based on urns, which mathematically leads to a theory of rational valued probabilities for finite possibility spaces.

Independently, in the 80’s, Nelson proposed a radically elementary probability theory based on real-valued probability mass functions for arbitrary possibility spaces, demonstrating this theory could recover, and simplify the formulation of, many important probabilistic results. This includes the functional central limit theorem that characterizes Brownian motion, and thereby Nelson removes all of the usual technicalities that arise in the measure theoretic approach to Brownian motion. Indeed, his approach needs no measure theory, a feature shared by the theories from De Finetti and Walley. Interestingly, Nelson’s approach also incorporates a fundamental notion of ambiguity, and embraces finite additivity, though these aspects are not often pointed out. Unfortunately, despite its beauty and elegance, Nelson’s programme failed to gain large traction to this day, perhaps partly because it relies on extending ZFC in a way that may first seem bizarre and counterintuitive.

In this talk, I revisit Lindley’s interpretation in the context of probability bounding. In doing so, I provide an alternative interpretation of lower previsions, which leads to new expressions for consistency (called avoiding sure loss) and inference (called natural extension). Unlike Walley’s approach, the duality theory that follows from this interpretation does not need the ultrafilter principle, and is purely constructive. A key corollary from these results is that every conditional probability measure (even finitely additive ones) can be represented by a net of probability mass functions, establishing that Nelson’s programme is universal: there is no probability measure that cannot be modelled by his approach. I reflect on what this means for practical probabilistic modelling and inference, and whether perhaps, in Nelson’s spirit, it is worthwhile to replace probability measures with probability mass functions as a foundation for probability and bounded probability, and to treat sigma-additivity as a sometimes welcome but often unnecessary by-product of idealization.

### On the interplay of optimal transport and distributionally robust optimization

Daniel Kuhn 12 December 2023Watch on YouTube

### Structural causal models are (solvable by) credal networks

Alessandro Antonucci 28 November 2023Watch on YouTube

### Falsification, Fisher's underworld of probability, and balancing behavioral & statistical reliability

Ryan Martin 18 October 2023Watch on YouTube

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.

There’s no paper yet on the exact contents of this talk, but some relevant material can be found at https: //arxiv.org/abs/2203.06703 and https://arxiv.org/abs/2211.14567.

### Application of uncertainty theory in the field of environmental risks

Dominique Guyonnet 27 September 2023Watch on YouTube

### One way to define an imprecise-probabilistic version of the Poisson process

Alexander Erreygers 16 June 2023Watch on YouTube

### Random fuzzy sets and belief functions: application to machine learning

Thierry Denœux 24 May 2023Watch on YouTube

### Some finitely additive probabilities and decisions

Teddy Seidenfeld 17 February 2023Watch on YouTube

### Engineering and IP: what's going on?

Alice Cicirello, Matthias Faes & Edoardo Pattelli 13 January 2023Watch on YouTube

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 2022Watch on YouTube

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

Ignacio Montes 21 October 2022Watch on YouTube

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.

### Imprecise probabilities in modern data science: challenges and opportunities

Ruobin Gong 29 June 2022Watch on YouTube

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

Gert de Cooman 30 May 2022Watch on YouTube