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
Falsification, Fisher's underworld of probability, and balancing behavioral & statistical reliability
Ryan Martin
18 October 2023, 15:00 CEST
Zoom link: https://utc-fr.zoom.us/j/82973185259Statisticians 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.
We present recent results on the intimate connections between causal inference and imprecise probabilities.
A structural causal model is made of endogenous (manifest) and exogenous (latent) variables.
We show that endogenous observations induce linear constraints on the probabilities of the exogenous variables.
This allows to map causal models to credal networks.
Causal inferences, such as interventions and counterfactuals, can be obtained by credal network algorithms.
These natively return sharp values in the identifiable case, while intervals corresponding to the exact bounds are produced for unidentifiable queries.
Exact computation will be inefficient in general, given that, as we show, causal inference is NP-hard, even for simple topologies.
We then target approximate bounds via a causal EM scheme.
We evaluate their accuracy by providing credible intervals on the quality of the approximation; we show through a synthetic benchmark that the EM scheme delivers accurate results in a fair number of runs.
We also present an actual case study on palliative care to show how our algorithms can readily be used for practical purposes.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.
Past Seminars
The management of environmental hazards is largely based on the assessment of risk; i.e., risk for human health and/or for ecosystems (water, soil, air, ...).
Environmental risks pertain to real-world systems that are typically incompletely known; hence risk is affected by significant uncertainty.
Historically, the treatment of uncertainties in risk assessments has relied largely on the use of oftentimes subjective single probability distributions.
Since around 30 years, alternative uncertainty theories have been applied, including the general framework of imprecise probabilities with, e.g., possibility theory and belief functions.
This presentation will provide specific examples of application of such uncertainty theories to environmental hazards, with a special focus on hazards related to soil and water pollution.
It will show how possibility theory and belief functions are well suited for representing information typically available in these contexts.
The issue of uncertainty propagation in risk assessment modelling will be addressed and also the question of communication on risk and associated uncertainties with third-party stakeholders.The Poisson process is one of the more fundamental continuous-time uncertain processes.
Besides its appearance in many applications, it is also interesting because there's several equivalent ways to define/construct it.
In this talk I will treat a couple of these definitions, will explain how I succeeded in generalising one of them to allow for imprecision, and will discuss how one could go about generalising the others.
Furthermore, I will explain how this work on the Poisson process fits in my more general push to advance the theory of Markovian imprecise (continuous-time) processes, and will touch on some (un)solved problems.The theory of belief functions is a powerful formalism for uncertain reasoning, with many successful applications to knowledge representation, information fusion, and machine learning.
Until now, however, most applications have been limited to problems (such as classification) in which the variables of interest take values in finite domains.
Although belief functions can, in theory, be defined in infinite spaces, we lacked practical representations allowing us to manipulate and combine such belief functions.
In this talk, I show that the theory of epistemic random fuzzy sets, an extension of Possibility and Dempster-Shafer theories, provides an appropriate framework for evidential reasoning in general spaces.
In particular, I introduce Gaussian random fuzzy numbers and vectors, which generalize both Gaussian random variables and Gaussian possibility distributions.
I then describe an application of this new formalism to nonlinear regression.Knightian Uncertainty in Finance and Economics
Frank Riedel
30 March 2023, 15:00 CET
Watch on YouTube