Mikael Jagan:
Midpoint-Radius Interval Arithmetic and R Package ‘flint’, an R Interface to the FLINT C Library

Interval arithmetic enables computation with automatic propagation of input error.  Defining interval arithmetic in arbitrary but finite precision (hence over a set of floating-point real numbers) raises interesting questions about how to represent intervals in memory and how to implement mathematical functions in light of tradeoffs between optimality of output and efficiency.  In the first half, I survey some of these issues, maintaining a focus on midpoint-radius interval arithmetic, also known as ball arithmetic, and its implementation in the Arb module of the FLINT C library. In the second half, I introduce R package 'flint', an R interface to FLINT, covering design principles, scope, usage, and future development.

Ivan Krylov:
Tensor Decompositions of Fluorescence Spectra: A Case Study in R

Excitation-emission fluorescence spectroscopy is a cheap and sensitive analysis method, which ensures its wide popularity in environmental monitoring. The structure of the resulting data makes it very amenable to tensor decompositions, specifically, PARAFAC, but the process involves a lot of important details. We will explore some of them, including data pre-treatment (surface interpolation), model validation (split-half), implementation and packaging in R (and some auxiliary packages), and take a look at problems still in need of a satisfactory solution, such as regularisation and expansions of the model.

Andreas Groll:
Fitting Regularized Partially Ordinal Regression Models With Don’t Know Option Within the GAMLSS Framework

This work deals with an extension of generalized additive models for analyzing regression data when the dependent variable is expressed by means of a partially ordered Likert scale including the "don't know" option. The proposed approach introduces a bivariate latent structure that jointly models the "don't know" decision and the subsequent ordinal response, allowing for flexible non-linear covariate effects and regularization. A central contribution is the use of regularization techniques to perform covariate selection and to distinguish informative predictors from noise in the presence of high-dimensional categorical variables. Estimation is carried out via a GAMLSS-based framework, enabling the combination of smooth terms, LASSO and LASSO group penalties, and fusion penalties. The model is evaluated through a simulation study and applied to the Italian Survey on Household Income and Wealth (SHIW), highlighting the role of geographic disparities and sociodemographic characteristics in shaping self-perceived income instability and the choice of the "don't know" option.

Bezirgen Veliyev:
Realized Principal Component Analysis of Noisy High-Frequency Data

In this paper, we propose a pre-averaging extension of Ait-Sahalia and Xiu (2019), who develop a realized principal component analysis for a continuous-time multi-dimensional log-price process observed discretely over a fixed time interval with vanishing mesh. It applies to study the eigenvalue problem for a time-varying covariance matrix when the high-frequency data are perturbed by measurement error. We derive a consistent noise-robust estimator of the spot covariance in a general framework. Then, exploiting the theory of volatility functional estimation of Jacod and Rosenbaum (2013), we design realized estimators of the integrated eigenvalue, eigenvector and principal component for this setting. We develop a fully-fledged mixed normal distribution theory for the eigenvalue estimator. It presents an asymptotic second-order bias that we show how to correct. In a Monte Carlo study, we document the accuracy of the realized eigenvalue within a standard linear factor model for asset pricing, while an empirical application illuminates its properties on stock market high-frequency data.

Co-authored with Francesco Benvenuti and Kim Christensen.

Antonio Peruzzi:
Media Bias and Polarization Through the Lens of a Markov Switching Latent Space Network Model

News outlets are now more than ever incentivized to provide their audience with slanted news, while the intrinsic homophilic nature of online social media may exacerbate polarized opinions. Here, we propose a new dynamic latent space model for time-varying online audience-duplication networks, which exploits social media content to conduct inference on media bias and polarization of news outlets. We contribute to the literature in several directions: 1) Our model provides a novel measure of media bias that combines information from both network data and text-based indicators; 2) we endow our model with Markov-Switching dynamics to capture polarization regimes while maintaining a parsimonious specification; 3) we contribute to the literature on the statistical properties of latent space network models. The proposed model is applied to a set of data on the online activity of national and local news outlets from four European countries in the years 2015 and 2016. We find evidence of a strong positive correlation between our media slant measure and a well-grounded external source of media bias. In addition, we provide insight into the polarization regimes across the four countries considered.

Paul Eisenberg:
Bounds for Expected Occupation Density and Applications

Occupation densities (local times) play a central role in the fine analysis of stochastic processes, providing a detailed description of how trajectories distribute mass in space and time. In this presentation, we discuss general bounds for expected occupation densities under minimal regularity and non-degeneracy assumptions. These results yield explicit estimates and clarify how probabilistic features of the underlying dynamics influence concentration behaviour.
We focus on applications to stochastic control problems and robust finance. In particular, we show how bounds on expected occupation densities provide a priori estimates for controlled dynamics, yielding effective control of state space exploration under admissible strategies and model uncertainty. These pre-estimates can be used to bound cost functionals, control constraint violations, and sensitivities with respect to changes in control policies or probability measures. Such results are especially useful in the analysis of existence, stability, and approximation of optimal controls, as well as in the design of numerical and learning-based methods in stochastic control and robust financial modelling.
Overall, the talk highlights expected occupation density estimates as a foundational probabilistic tool for deriving robust pre-estimates in stochastic control and related areas.

Rüdiger Frey: 
A Mean-Field Game Analysis of Systemic Risk under Capital Constraints

We analyze the effect of regulatory capital constraints on financial stability in a large homogeneous banking system using a mean-field game (MFG) model.  Each bank holds cash and a tradable risky asset. Banks choose absolutely continuous trading rates in order to maximize expected terminal equity, with trades subject to transaction costs. Capital regulation requires equity to exceed a fixed multiple of the position in the tradable asset; breaches trigger forced liquidation. The  asset drift depends on changes in average asset holdings across banks, so aggregate deleveraging creates contagion  effects, leading to an MFG.  We discuss the coupled forward–backward PDE system characterizing equilibria of the MFG, and we solve the constrained MFG numerically.  Experiments demonstrate that capital constraints accelerate deleveraging and limit risk-bearing capacity. In some regimes, simultaneous breaches trigger liquidation cascades.
The last part of the presentation is devoted to the mathematical analysis of a model with time-smoothed contagion as in, e.g., Hambly, Ledger and Sojmark (2019) or Campi and Burzoni (2024). We characterize optimal strategies for a given evolution of the system and establish the existence of an MFG equilibrium.

Gregor Kastner:
Bayesian Nonparametric Priors for Model-Based (Partial) Clustering

We discuss variations of prior distributions for finite and potentially infinite mixture models. First, we extend standard Bayesian nonparametric spatial priors to additionally incorporate the temporal dimension, thereby allowing for spatio-temporal clustering. Second, we show how these priors can be modified to cater for partial effects by a priori distinguishing between control and target variables. Third, we propose a novel prior for modeling the weights in mixture models. It is based on the Selberg Dirichlet distribution, an extension of the standard Dirichlet with a repulsive term, and penalizes mixture weights that lie close to each other. The approaches are illustrated with applications from various fields: modeling unemployment, quantifying the effect of European agricultural subsidies, and uncovering patterns in biomedical data.