Pleanary talks will be given in the main conference hall and have duration 50′ for the talk and 10′ for questions and discussion.
Talk Title: Some statistical insights into physics-informed neural networks
Physics-informed neural networks (PINNs) are a promising approach that combines the power of neural networks with the interpretability of physical modeling. PINNs have shown good practical performance in solving partial differential equations (PDEs) and in hybrid modeling scenarios, where physical models enhance data-driven approaches. However, it is essential to establish their theoretical properties in order to fully understand their capabilities and limitations. In this talk, I will highlight that classical training of PINNs can suffer from systematic overfitting. This problem can be addressed by adding a ridge regularization to the empirical risk, which ensures that the resulting estimator is risk-consistent for both linear and nonlinear PDE systems. However, the strong convergence of PINNs to a solution satisfying the physical constraints requires a more involved analysis using tools from functional analysis and calculus of variations. In particular,for linear PDE systems, an implementable Sobolev-type regularization allows to reconstruct a solution that not only achieves statistical accuracy but also maintains consistency with the underlying physics.
Talk Title: Opinion dynamics on complex networks: From mean-field limits to sparse approximations
In a world of polarized opinions on many cultural issues, we propose a model for the evolution of opinions on a large complex network. Our model is akin to the popular Friedkin-Johnsen model, with the added complexity of vertex-dependent media signals and confirmation bias, both of which help explain some of the most important factors leading to polarization. The analysis of the model is done on a directed random graph, capable of replicating highly inhomogeneous real-world networks with various degrees of assortativity and community structure. Our main results give the stationary distribution of opinions on the network, including explicitly computable formulas for the conditional means and variances for the various communities. Our results span the entire range of inhomogeneous random graphs, from the sparse regime, where the expected degrees are bounded, all the way to the dense regime, where a graph having n vertices has order n2 edges.
Talk Title: Repeated Significance Tests Based on Multiple Scan Statistics for One- and Two-Dimensional Data
In this lecture multiple scan statistics for one- and two-dimensional data will be reviewed. Repeated Significance Tests (RST) based on multiple scan statistics will be introduced for one- and two dimensional discrete and continuous data. The implementation of these RST’s for a specified significance level will be discussed. Numerical results for expected stopping times and power will be presented, for specified null hypotheses and selective alternatives. The simulation algorithms for implementing the RST’s will be discussed as well.
Talk Title: Markov Chain Monte Carlo Meets Generative AI
Deep generative models parameterize very flexible families of distributions capable of fitting complicated image or text datasets. These models provide independent samples from complex high-dimensional distributions at affordable cost. On the other hand, accurately sampling a target distribution, such as a Bayesian posterior in inverse problems, is typically challenging: either due to dimensionality, multimodality, poor conditioning, or a combination of the aforementioned factors. In this talk, I will discuss recent works that attempt to improve traditional inference and sampling algorithms through learning. I will present flowMC, an adaptive MCMC with normalizing flows, along with initial applications and remaining challenges.
Talk Title: Stationary states and exit times for Lévy processes with partial resetting
Talk Title: Perspectives on Mortality Modelling
This presentation will discuss and analyse national level demographics that have led to recent developments in new statistical modelling approaches to mortality forecasting and life-table estimation. This is important to actuarial science as such quantities often act as critical components of decision making on pension provision and planning, mortality linked financial securities and life insurance products.
In particular, I will discuss aspects of some recent research papers covering time-series regression modelling
that incorporates key population modelling components such as, temporal graduation, period effects, cohort
effects and persistence (long memory) in order to enhance national level, age and gender stratified mortality
forecasting. These may be considered as important extensions to the classical GLM regression structures and
Lee-Carter stochastic mortality models often used by actuaries in practice to undertake mortality projection.
The improvements introduced are demonstrated to help to tackle a key concern raised by the IMF and some
national demographic and national statistics agencies that in recent years the classical actuarial mortality
projections using standard Lee-Carter or GLM frameworks are beginning to produce under estimation of
mortality projections. This can have profound ramifications for governments and private pension providers and
life-insurance providers.
1.Fung M.C., Peters G.W. and Shevchenko P.V. (2017) A Unified Approach to Mortality Modelling
using State-Space Framework: Characterisation, Identification, Estimation and Forecasting.
Annals of Actuarial Science, May 1-47. (SSRN index: ssrn.2786559)
2. Fung M.C., Peters G.W. and Shevchenko P.V. (2018) Cohorot Effects in Mortality Modelling: A
Bayesian State-Space Approach. Annals of Actuarial Science, March 1-40. (SSRN index:
ssrn.2786559)
3. Toczydlowska D., Peters G.W., Fung M.C. and Shevchenko P.V. (2018) Stochastic Period and
Cohort Effect State-Space Mortality Models Incorporating Demographic Factors via
Probabilistic Robust Principle Components. Risk, 5(3), 1-77. (SSRN index: ssrn.2977306)
4. Yan H., Peters G.W. and Chan J. (2019) Multivariate Long Memory Cohort Mortality Models.
ASTIN Bulletin. (SSRN index: ssrn.3166884)
5. Yan H., Peters G.W. and Chan J. (2020) Mortality Models Incorporating Long Memory Improves
Life Table Estimation: A Comprehensive Analysis. Annals of Actuarial Science. (SSRN index:
ssrn.3149914)
6. Peters G.W., Yan H. and Chan J. (2020) Evidence for Persistence and Long Memory Features in
Mortality Data Annals of Actuarial Science. (SSRN index: ssrn.3322611)
Talk Title: Weak Ergodicity in General Non-Homogeneous Markov System
We start with the definition of the new concept of the General NonHomogeneous Markov System (G-NHMS) and give the expected population structure of a NHMS in the various states given the transition probability matrices of the memberships. We proceed by establishing the set of all possible expected relative distributions of the initial number of 
