Programme CRiSM 2.0 - Conference 2025

All talks will be held in rooms in the Zeeman BuildingLink opens in a new window (Mathematics) and MSB BuildingLink opens in a new window (Statistics). The Registration and coffee breaks on Wednesday will be held in "The Street", in front of Zeeman room MS.01. All lunches, poster session, wine and food reception will be held in "The Atrium", the main foyer in the MSB BuildingLink opens in a new window. A schedule of the main conference is given below.

**Update post-conference: slides which have been kindly shared can be found linked from the talk titles below.**

Schedule

Day	Time	Activity/ Speakers	Location (all Sessions in Zeeman)
Wednesday 21 May	14:30 - 15:00	Registration and Coffee	The Street (Zeeman)
	15:00 - 16:00	Keynote Lecture Regina Liu: Fusion Learning: Combining inferences from diverse data sources	MS.01
	16:00 - 16:45	Parallel Session A (Statistical theory & application) Judith Rousseau: Bayesian estimation in high dimensional Hawkes processes Parallel Session B (Probability) Dario Spanò: Excursion theory of Wright-Fisher diffusions	MS.01 MS.05
	16:45 - 17:30	Parallel Session C (Computational statistics & machine learning) Alexandros Beskos: A closed-form transition density expansion for elliptic and hypo-elliptic SDEs Parallel Session D (Mathematical finance) Luitgard Veraart: Modelling contagious bank runs	MS.01 MS.05
	18:00 - 21:00	Wine Reception and Posters	The Atrium (MSB)

Thursday 22 May	09:00 - 10:00	Keynote Lecture Jan Obłój: X-OT: on variants of optimal transport problem and understanding model robustness	MS.01
	10:00 - 10:45	Parallel Session D (Mathematical finance) Nicole Bäuerle: Relative portfolio optimization Parallel Session A (Statistical theory & application) Ioannis Kosmidis: Penalized likelihood estimation and inference in high-dimensional logistic regression	MS.01 MS.04
	10:45 - 11:15	Coffee Break	The Street (Zeeman)
	11:15 - 12:00	Parallel Session B (Probability) Cecile Mailler: A localisation phase transition for the catalytic branching random walk Parallel Session C (Computational statistics & machine learning) Anthony Lee: Explicit convergence bounds for Metropolis Markov chains: isoperimetry, spectral gaps and profiles	MS.01 MS.04
	12:00 - 12:45	Parallel Session D (Mathematical finance) Yufei Zhang: alpha-potential games: A new paradigm for N-player dynamic games Parallel Session A (Statistical theory & application) Amy Wilson: Statistics and the law: what’s the verdict?	MS.01 MS.04
	12:45 - 14:15	Lunch	The Atrium (MSB)
	14:15 - 15:15	Keynote Lecture George Deligiannidis: Theory for denoising diffusion models and the manifold hypothesis	MS.01
	15:15 - 16:00	Parallel Session C (Computational Statistics & machine learning) Chris Oates: Probabilistic Richardson extrapolation Parallel Session B (Probability) Sunil Chhita: The two-periodic Aztec diamond	MS.01 MS.04
	16:00 - 16:20	Coffee Break	The Street (Zeeman)
	16:20 - 17:05	Parallel Session A (Statistical theory & application) John Aston: Using geometry in non-parametric statistics Parallel Session D (Mathematical finance) Martin Herdegen: Risk, utility and sensitivity to large losses	MS.01 MS.04
	19:00	Dinner by invitation only	Scarman
Friday 23 May	09:00 - 10:00	Keynote Lecture Philip Ernst: Yule's "nonsense correlation": Moments and density	MS.01
	10:00 - 10:45	Parallel Session B (Probability) Emma Horton: Conditioned exit measures of non-local branching processes Parallel Session C (Computational Statistics & machine learning) Alice Peng: A computational cell-based model for contraction of burns with parameter sensitivity analysis and finite-element methods	MS.01 MS.04
	10:45 - 11:15	Coffee Break	The Street (Zeeman)
	11:15 - 12:00	Parallel Session D (Mathematical finance) Michalis Zervos: Market equilibrium under proportional transaction costs in a stochastic factor model Parallel Session C (Computational statistics & machine learning) Francesca Crucinio: Interacting particle algorithms for maximum likelihood estimation	MS.01 MS.04
	12:00 - 12:45	Parallel Session B (Probability) Krzysztof Łatuszyński: Bernoulli factories, dice enterprises and more - probability problems born in computational Bayesian inference Parallel Session A (Statistical theory & application) Helen Ogden: Flexible models for simple longitudinal data	MS.01 MS.04
	12:45 - 13:00	Closing Remarks with a light lunch after in the foyer 'The Street'	MS.01

Speakers, titles, and abstracts

Statistical theory and application

Regina LiuLink opens in a new window (Keynote Speaker) (Rutgers University) - Fusion Learning: combining inferences from diverse data sources
Advanced data acquisition technology nowadays has often made inferences from diverse data sources easily accessible. Fusion learning refers to combining inferences from multiple sources or studies to make a more effective overall inference. We focus on the tasks: 1) Whether/When to combine inferences? 2) How to combine inferences efficiently? 3) How to combine inference to enhance an individual study, thus named i-Fusion?
We present a general framework for nonparametric and efficient fusion learning for inference on multi-parameters, which may be correlated. The main tool underlying this framework is the new notion of depth confidence distribution (depth-CD), which is developed by combining data depth, bootstrap and confidence distributions. We show that a depth-CD is an omnibus form of confidence regions, whose contours of level sets shrink toward the true parameter value, and thus an all-encompassing inferential tool. The approach is shown to be efficient, general and robust. It readily applies to heterogeneous studies with a broad range of complex and irregular settings. This property also enables the approach to utilize indirect evidence from incomplete studies to gain efficiency for the overall inference. The approach is demonstrated with simulation studies and real applications in tracking aircraft landing performance and in zero-event studies in clinical trials.
This is joint work with Dungang Liu (U. Cincinnati, Lindner College of Business) and Minge Xie (Rutgers University).

John AstonLink opens in a new window (University of Cambridge) - Using geometry in non-parametric statistics
In non-parametric regression, the rates of estimation critically depend on the dimension, usually known as the curse of dimensionality. However, it has been long known that incorporating structure into the regression (such as sparsity) can improve on general rates. However, sparsity and most related concepts are linear in the data, while many patterns in regressions are non-linear in nature, and crucially depend on all the covariates. In this talk, we will consider how more general structure can be incorporated in non-parametric regression through the use of symmetries. General notions of symmetry corresponding to algebraic group structures can exhibit the similar dimension reduction phenomena, even in non-linear settings, and even in the case where the symmetries need to be estimated as part of the regression. We will also show that, by considering lattice structures, efficient computational estimation schemes to determine such symmetries are possible. This is joint work with Louis Christie (Cambridge).

Ioannis KosmidisLink opens in a new window (University of Warwick) - Penalized likelihood estimation and inference in high-dimensional logistic regression
In recent years, there has been a surge of interest in estimators and inferential procedures that exhibit optimal asymptotic properties in high-dimensional logistic regression when the number of covariates grows proportionally as a fraction ($\kappa \in (0,1)$) of the number of observations. In this seminar, we focus on the behaviour of a class of maximum penalized likelihood estimators, employing the Diaconis-Ylvisaker prior as the penalty.
Building on advancements in approximate message passing, we analyze the aggregate asymptotic behaviour of these estimators when covariates are normal random variables with arbitrary covariance. This analysis enables us to eliminate the persistent asymptotic bias of the estimators through straightforward rescaling for any value of the prior hypertuning parameter. Moreover, we derive asymptotic pivots for constructing inferences, including adjusted Z-statistics and penalized likelihood ratio statistics.
Unlike the maximum likelihood estimate, which only asymptotically exists in a limited region on the plane of $\kappa$ versus signal strength, the maximum penalized likelihood estimate always exists and is directly computable via maximum likelihood routines. As a result, our asymptotic results remain valid even in regions where existing maximum likelihood results are not obtainable, with no overhead in implementation or computation.
The dependency of the estimators on the prior hyper-parameter facilitates the derivation of estimators with zero asymptotic bias and minimal mean squared error. We will explore these estimators' shrinkage properties, substantiate our theoretical findings with simulations and applications, and present evidence for conjectures with different penalties, such as Jeffreys' prior and non-normal covariate distributions.
Collaborators: Philipp Sterzinger and Patrick Zietkiewicz
Preprints: https://arxiv.org/abs/2311.07419, https://arxiv.org/abs/2311.11290

Helen OgdenLink opens in a new window (University of Southampton) - Flexible models for simple longitudinal data
I will describe a new method for modelling simple longitudinal data. We aim to do this in a flexible manner (without restrictive assumptions about the shapes of individual trajectories), while exploiting structural similarities between the trajectories. Hierarchical models (such as linear mixed models, generalised additive mixed models and hierarchical generalised additive models) are commonly used to model longitudinal data, but fail to meet one or other of these requirements: either they make restrictive assumptions about the shape of individual trajectories, or fail to exploit structural similarities between trajectories. Functional principal components analysis promises to fulfil both requirements, and methods for functional principal components analysis have been developed for longitudinal data. However, we find that existing methods sometimes give poor-quality estimates, particularly when the number of observations on each individual is small.
In our new approach, hierarchical modelling with functional principal components, inference is conducted based on the full likelihood of all unknowns, with a penalty term to control the balance between fit to the data and smoothness of the trajectories. I will present simulation studies to demonstrate that the new method substantially improves the quality of inference relative to existing methods across a range of examples, and apply the method to data on changes in body composition in adolescent girls.

Judith RousseauLink opens in a new window (University of Oxford/Université Paris Dauphine) - Bayesian estimation in high dimensional Hawkes processes
Multivariate Hawkes processes form a class of point processes describing self and inter exciting/inhibiting processes. There is now a renewed interest in such processes in applied domains and in machine learning, but there exists only limited theory about inference in such models, in particular in high dimensions.
To be more precise, the intensity function of a linear Hawkes process has the following form: for each dimension $k \leq K$
\[ \lambda^k(t) = \sum_{\ell \leq K} \int_0^{t^-} h_{\ell k}(t - s) dN_s^\ell + \nu_k, \quad t \in [0, T] \]
where $(N^\ell, \ell \leq K)$ is the Hawkes process and $\nu_k > 0$. There have been some recent theoretical results on Bayesian estimation in the context of linear and nonlinear multivariate Hawkes processes, but these results assumed that the dimension K was fixed. Convergence rates were studied assuming that the observation window T goes to infinity.
In this work, we consider the case where K is allowed to go to infinity with T. We consider generic conditions to obtain posterior convergence rates, and we derive, under sparsity assumptions, convergence rates in L1 norm and consistent estimation of the graph of interactions.
This is joint work with Vincent Rivoirard and Deborah Sulem.

Amy WilsonLink opens in a new window (University of Edinburgh) - Statistics and the law: what’s the verdict?
Criminal cases can feature multiple pieces of dependent evidence and multiple possible explanations for this evidence. It can be challenging to disentangle the correlations between pieces of evidence and to understand how to form a logically consistent argument that accounts for this evidence in a way that is probabilistically sound. There have been high profile miscarriages of justice that have resulted from failures in probabilistic reasoning and interpretation.
In this talk I will show how chain event graphs can be used to construct possible storylines for displaying the time evolution of events and evidence in criminal cases. These chain event graphs can both be used to investigate possible arguments when drawing up a case and to make probabilistic assessments of the strength of evidence when prosecuting or defending. I will give two examples - a drugs on banknotes case and the case of the murder of Meredith Kercher. To finish the talk I will discuss the role that statistics and probabilistic reasoning can play in criminal cases and highlight where greater collaboration is needed between statisticians and those in the legal sector.

Computational statistics and machine learning

George DeligiannidisLink opens in a new window (Keynote speaker) (University of Oxford) - Theory for denoising diffusion models and the manifold hypothesis
Denoising diffusion models (DDMs) is a class of generative models that works by corrupting data with noise and learning to reverse this noising process in order to generate fresh samples from an approximation of the data distribution. They achieve state-of-the-art results in image, audio and video generation. Their great empirical success is not yet fully understood, but is conjectured to stem in part from the ability of DDMs to adapt to low-dimensional geometric structures in the data. I will present some recent results that support this conjecture, in particular convergence rates for DDMs that scale with the dimension of the sub-manifold where the data lives, instead of the ambient dimension, which may be orders of magnitude larger.

Alexandros BeskosLink opens in a new window (University College London) - A closed-form transition density expansion for elliptic and hypo-elliptic SDEs
We introduce a closed-form expansion for the transition density of elliptic and hypo-elliptic multivariate Stochastic Differential Equations (SDEs), over a period $\Delta\in (0,1)$, in terms of powers of $\Delta^{k/2}$, $k\ge 0$. Our methodology provides approximations of the transition density, easily evaluated via any software that performs symbolic calculations. A major part of the paper is devoted to an analytical control of the remainder in our expansion for fixed $\Delta\in(0,1)$. The obtained error bounds validate the methodology, by characterising the size of the distance from the true value. It is the first time that such a closed-form expansion becomes available for the important class of hypo-elliptic SDEs, to the best of our knowledge. For elliptic SDEs, closed-form expansions are available, with some works identifying the size of the error for fixed $\Delta$, as per our contribution. Our methodology allows for a uniform treatment of elliptic and hypo-elliptic SDEs, when earlier works are intrinsically restricted to an elliptic setting. We show numerical applications highlighting the effectiveness of our method, by carrying out parameter inference for hypo-elliptic SDEs that do not satisfy stated conditions. The latter are sufficient for controlling the remainder terms, but the closed-form expansion itself is applicable in general settings.

Francesca CrucinioLink opens in a new window (King's College London) - Interacting particle algorithms for maximum likelihood estimation
We introduce a class of algorithms for inference and learning in latent variable models whose joint probability density is non-differentiable. Leveraging proximal Markov chain Monte Carlo (MCMC) techniques and the recently introduced interacting particle Langevin algorithm (IPLA), we propose several variants within the novel proximal IPLA family, tailored to the problem of estimating parameters in a non-differentiable statistical model. We prove nonasymptotic bounds for the parameter estimates produced by the different algorithms in the strongly log-concave setting and provide comprehensive numerical experiments on various models to demonstrate the effectiveness of the proposed methods. In particular, we demonstrate the utility of our family of algorithms on a toy hierarchical example where our assumptions can be checked, as well as for sparse Bayesian logistic regression, training of sparse Bayesian neural networks, and sparse matrix completion. Our theory and experiments together show that PIPLA family can be the de facto choice for parameter estimation problems in non-differentiable latent variable models.

Anthony LeeLink opens in a new window (University of Bristol) - Explicit convergence bounds for Metropolis Markov chains: isoperimetry, spectral gaps and profiles
We derive the first explicit bounds for the spectral gap of a random walk Metropolis algorithm on R^d for any value of the proposal variance, which when scaled appropriately recovers the correct 1/d dependence on dimension for suitably regular invariant distributions. We also obtain explicit bounds on the L2-mixing time for a broad class of models. In obtaining these results, we refine the use of isoperimetric profile inequalities to obtain conductance profile bounds, which also enable the derivation of explicit bounds in a much broader class of models. We also obtain similar results for the preconditioned Crank--Nicolson Markov chain, obtaining dimension-independent bounds under suitable assumptions.

Chris OatesLink opens in a new window (Newcastle University) - Probabilistic Richardson extrapolation
For over a century, extrapolation methods have provided a powerful tool to improve the convergence order of a numerical method. However, these tools are not well-suited to modern computer codes, where multiple continua are discretised and convergence orders are not easily analysed. To address this challenge we present a probabilistic perspective on Richardson extrapolation, a point of view that unifies classical extrapolation methods with modern multi-fidelity modelling, and handles uncertain convergence orders by allowing these to be statistically estimated. The approach is developed using Gaussian processes, leading to Gauss-Richardson Extrapolation (GRE). Conditions are established under which extrapolation using the conditional mean achieves a polynomial (or even an exponential) speed-up compared to the original numerical method. Further, the probabilistic formulation unlocks the possibility of experimental design, casting the selection of fidelities as a continuous optimisation problem which can then be (approximately) solved. A case-study involving a computational cardiac model demonstrates that practical gains in accuracy can be achieved using the GRE method.

Alice PengLink opens in a new window (Lancaster University) - A computational cell-based model for contraction of burns with parameter sensitivity analysis and finite-element methods
Deep tissue injury, such as severe burns, often go with the contraction of skin. This contraction can become problematic if it causes loss of mobility of the joint of the patient. Our final objective is to predict the likelihood that such a contracture occurs and to analyze the impact of several treatments on the likelihood of the development of a serious contraction. To do so, we develop a mathematical framework based on tracking the migration and proliferation of individual cells, especially immune cells and fibroblasts. Furthermore, we take into account the forces that are exerted by the (myo)fibroblasts on their environment. This results into a stochastic finite element framework that eventually will be used to estimate the probability of an occurring contraction.

To investigate the correlations between the parameters and the outcomes, such as healing time and severity of the contraction, Monte Carlo simulations are conducted for the parameter sensitivity analysis. We observed a high correlation between the wound area after 4 days and the final/minimal wound area, which indicates the possibility for clinical staff to predict the ultimate contraction and then interfere the healing process in time.

Probability

Philip ErnstLink opens in a new window (Keynote Speaker) (Imperial College London) - Yule's "nonsense correlation": Moments and density
In 1926, G. Udny Yule considered the following problem: given two independent and identically distributed random walks independent from each other, what is the distribution of their empirical correlation coefficient? Yule empirically observed the distribution of this statistic to be heavily dispersed and frequently large in absolute value, leading him to call it "nonsense correlation." This unexpected finding led to his formulation of two concrete questions, each of which would remain open for more than ninety years: (i) Find (analytically) the variance of this empirical correlation coefficient and (ii): Find (analytically) the higher order moments and the density of this empirical correlation coefficient. After giving a brief overview of the solution to question (i) in Ernst et al. (The Annals of Statistics, 2017), we turn to the recent work of Ernst et al. (Bernoulli, 2025), which closed question (ii) by explicitly calculating all moments of the empirical correlation coefficient (up to order 16). This leads, for the first time, to an approximation to the density of Yule's nonsense correlation. The methodology of Ernst et al. (2025) further enables explicit calculations of the moments of the empirical correlation coefficient when the two independent Wiener processes are replaced by two correlated Wiener processes, two independent Ornstein-Uhlenbeck processes, and two independent Brownian bridges. We also succeed in proving a Central Limit Theorem for the case of two independent Ornstein-Uhlenbeck processes. This shows that Yule's "nonsense correlation", is indeed not "nonsense" for stochastic processes which admit stationary distributions.

Sunil ChhitaLink opens in a new window (Durham University) - The two-periodic Aztec diamond
The two-periodic Aztec diamond is a random tiling model which features three macroscopic regions known as frozen, rough and smooth, which are each characterized by their decay of correlations. In this talk, we will introduce the model as well as describe the behavior at the rough-smooth boundary. This talk is based on work in progress with Duncan Dauvergne and Thomas Finn.

Emma HortonLink opens in a new window (University of Warwick) - Conditioned exit measures of non-local branching processes
Motivated by the need to estimate rare event probabilities in fissile systems, we consider path decompositions for conditioned exit measures of non-local branching processes. In particular, we show that non-local branching processes conditioned to exit a domain via certain sets exhibit a many-to-few decomposition.

Krzysztof ŁatuszyńskiLink opens in a new window (University of Warwick) - Bernoulli factories, dice enterprises and more - probability problems born in computational Bayesian inference
Given a p-coin that lands heads with unknown probability p, we wish to produce an f(p)-coin for a given function f:(0,1)->(0,1). This seemingly simple problem poses a challenge in Bayesian inference for intractable likelihood models. At the same time, it is a celebrated problem in probability, which can be traced back to Jon von Neumann, and is known as the Bernoulli Factory. Generic ways to design a practical Bernoulli factory for a given function f exist only in a few special cases. In this talk, I will explain how the Bernoulli Factory type problems arise in Bayesian inference, explain the efficiency motivation behind solving them and then I will present a constructive way to build an efficient Bernoulli factory when f(p) is a rational function with coefficients in R. Moreover, I extend the Bernoulli factory problem to a more general setting where we have access to an m-sided die and we wish to roll a v-sided one; that is, we consider rational functions between open probability simplices. This work is based on a series of papers in both probability and statistical inference.

Cecile MaillerLink opens in a new window (University of Bath) - A localisation phase transition for the catalytic branching random walk
In this joint work with Bruno Schapira, we show the existence of a phase transition between a localisation and a non-localisation regime for a branching random walk with a catalyst at the origin. More precisely, we consider a continuous-time branching random walk that jumps at rate one, with simple random walk jumps on Z^d, and that branches (with binary branching) at rate lambda>0 everywhere, except at the origin, where it branches at rate lambda_0 > lambda. We show that, if lambda_0 is large enough, then the occupation measure of the branching random walk localises (i.e. converges almost surely without spatial renormalisation), whereas, if lambda_0 is close enough to lambda, then localisation cannot occur, at least not in a strong sense.

Dario SpanòLink opens in a new window (University of Warwick) - Excursion theory of Wright-Fisher diffusions
Motivated by statistical applications, I will illustrate aspects of excursion theory for the Wright–Fisher diffusion with recurrent mutation, a fundamental model in population genetics. The structure is intermediate between the classical excursion theory, where all excursions begin and end at a single point, and the more general approach considering excursions of processes from general sets. Since the Wright–Fisher diffusion has two boundary points, it is natural to construct excursions which start from a specified boundary point, and end at one of two boundary points which determine the next starting point. Several identities for excursion measures and hitting time distributions will be described both via special function theory and via the coalescent dual.

Mathematical finance

Jan ObłójLink opens in a new window (Keynote Speaker) (University of Oxford) - X-OT: on variants of optimal transport problem and understanding model robustness
Across vast array of applications, mathematics is used to build models which create pathways from inputs to outputs. These models can often be seen as probability measures: discrete (empirical measures over a given data set) or continuous (resulting from an SDE), over finite-dimensional spaces or over pathspaces. The theory of Optimal Transport (OT) offers powerful fully non-parametric tools to measure distances between probability measures, trace geodesics in the space of probability measures, project onto its subsets. In this talk, I will survey some recent advancements that leverage OT tools and intuition, to describe and manage models, helping with selecting/calibrating models and quantifying model uncertainty. I will use questions from mathematical finance as my motivating examples while focusing on providing an overview of the field with its novel mathematical contributions, including several variants of the classical OT paradigm, and ongoing challenges. In particular, I will discuss robust pricing and hedging and its link to Martingale-OT, non-parametric calibration via Semimartingale-OT, and Wasserstein distributionally robust optimization and the resulting non-parametric Greeks and risk measurements. I will also mention some applications in statistics and machine learning, including adversarial robustness of DNNs.
The talk is based on works with many collaborators, including: D. Bartl, S. Drapeau, S. Eckstein, G. Guo, I. Guo, Y. Jiang, B. Joseph, T. Lim, G. Loeper, S. Wang and J. Wiesel.

Nicole BäuerleLink opens in a new window (Karlsruhe Institute of Technology) - Relative portfolio optimization
Within a common arbitrage-free semimartingale financial market we consider the problem of determining all Nash equilibrium investment strategies for $n$ agents who try to maximize the expected utility of their relative wealth. The utility function can be rather general here. Exploiting the linearity of the stochastic integral and making use of the classical pricing theory we are able to express all Nash equilibrium investment strategies in terms of the optimal strategies for the classical one agent expected utility problems. The corresponding mean field problem is solved in the same way. We give applications to specific financial markets and compare our results with those given in the literature. Moreover, we also consider the problem of determining all Nash equilibrium investment strategies for $n$ agents who try to maximize the expected utility of their wealth under the constraint that with certain probability the own wealth exceeds a linear combination of the others. We compare the investment strategy to the optimal one without competition. (Joint work with T. Göll)

Martin HerdegenLink opens in a new window (University of Stuttgart) - Risk, utility and sensitivity to large losses
Risk and utility functionals are fundamental building blocks in economics and finance. In this paper we investigate under which conditions a risk or utility functional is sensitive to the accumulation of losses in the sense that any sufficiently large multiple of a position that exposes an agent to future losses has positive risk or negative utility. We call this property sensitivity to large losses and provide necessary and sufficient conditions thereof that are easy to check for a very large class of risk and utility functionals. In particular, our results do not rely on convexity and can therefore also be applied to most examples discussed in the recent literature, including (non-convex) star-shaped risk measures or $S$-shaped utility functions encountered in prospect theory. As expected, Value at Risk generally fails to be sensitive to large losses. More surprisingly, this is also true of Expected Shortfall. By contrast, expected utility functionals as well as (optimized) certainty equivalents are proved to be sensitive to large losses for many standard choices of concave and nonconcave utility functions, including $S$-shaped utility functions. We also show that Value at Risk and Expected Shortfall become sensitive to large losses if they are either properly adjusted or if the property is suitably localized.
The talk is based on joint work with Nazem Khan (University of Oxford) and Cosimo Munari (University of Verona).

Luitgard VeraartLink opens in a new window (London School of Economics and Political Science) - Modelling contagious bank runs
We develop a modelling framework for contagion in financial networks arising from bank runs. We show how interacting channels of contagion, namely funding withdrawals in the interbank network and price-mediated contagion arising from fire sales can turn a bank run on one institution into a systemic crisis. Furthermore, we also model how contagion effects can lead to additional bank runs. Our model allows for a wide range of withdrawal mechanisms both by banks and by external depositors.
It can be used for financial stress testing and particularly for analysing implications of different withdrawal mechanisms for systemic risk. We illustrate this in stylised examples and an empirical case study. We find that the extent of systemic risk is highly sensitive to the choices of withdrawal strategies used by the market participants. We also discuss policy implications.

Michalis ZervosLink opens in a new window (London School of Economics and Political Science) - Market equilibrium under proportional transaction costs in a stochastic factor model
We consider an economy with two agents. Each of the two agents receives a random endowment flow. We model this cumulative flow as the stochastic integral of a deterministic function of the economy's state, which we model by means of a general Ito diffusion. Each of the two agents has mean-variance preferences with different risk-aversion coefficients. The two agents can also trade a risky asset. We determine the agents' optimal equilibrium trading strategies in the presence of proportional transaction costs. In particular, we derive a new free-boundary problem that provides the solution to the agents' optimal equilibrium problem. Furthermore, we derive the explicit solution to this free-boundary problem when the problem data is such that the frictionless optimiser is a strictly increasing or a strictly increasing and then strictly decreasing function of the economy's state.

Yufei ZhangLink opens in a new window (Imperial College London) - $alpha$ -potential games: A new paradigm for $N$ -player dynamic games

Static potential games, pioneered by Monderer and Shapley (1996), are non-cooperative games in which there exists an auxiliary function called static potential function, so that any player's change in utility function upon unilaterally deviating from her policy can be evaluated through the change in the value of this potential function. The introduction of the potential function is powerful as it simplifies the otherwise challenging task of finding Nash equilibria for non-cooperative games: maximizers of potential functions lead to the game's Nash equilibria.
In this talk, we propose an analogous and new framework called $\alpha$-potential game for dynamic $N$-player games, with the potential function in the static setting replaced by an $\alpha$-potential function. We present an analytical characterization of $\alpha$-potential functions for any dynamic game. For stochastic differential games in which the state dynamic is a controlled diffusion, $\alpha$ is explicitly identified in terms of the number of players, and the intensity of interactions and the level of heterogeneity among players. We further show the $\alpha$-Nash equilibrium of the stochastic game can be constructed through an associated conditional McKean-Vlasov control problem. To illustrate our findings, we examine a linear-quadratic game on a graph, where $\alpha$ captures asymmetric interactions and player heterogeneity beyond the mean-field paradigm.

Poster contributions

Matthew Adeoye (University of Warwick) - Bayesian spatio-temporal modelling for infectious disease outbreak detection
The Bayesian analysis of infectious disease surveillance data from multiple locations typically involves building and fitting a spatio-temporal model of how the disease spreads in the structured population. Here we present new generally applicable methodology to perform this task. We introduce a parsimonious representation of seasonality and a biologically informed specification of the outbreak component to avoid parameter identifiability issues. We develop a computationally efficient Bayesian inference methodology for the proposed models, including techniques to detect outbreaks by computing marginal posterior probabilities at each spatial location and time point. We show that it is possible to efficiently integrate out the discrete parameters associated with outbreak states, enabling the use of dynamic Hamiltonian Monte Carlo (HMC) as a complementary alternative to a hybrid Markov chain Monte Carlo (MCMC) algorithm. Furthermore, we introduce a robust Bayesian model comparison framework based on importance sampling to approximate model evidence in high-dimensional space. The performance of our methodology is validated through systematic simulation studies, where simulated outbreaks were successfully detected, and our model comparison strategy demonstrates strong reliability. We also apply our new methodology to monthly incidence data on invasive meningococcal disease from 28 European countries. The results highlight outbreaks across multiple countries and months, with model comparison analysis showing that the new specification outperforms previous approaches.

Nicola Branchini (University of Edinburgh) - Revisiting SNIS: new methods and diagnostics
Importance sampling (IS) can often be implemented only with normalized weights, yielding the popular self-normalized IS (SNIS) estimator. Yet, proposal distributions are usually learned and evaluated using criteria designed for the unnormalized IS (UIS) estimator. We aim to present a unified perspective on our recent advances in understanding and improving SNIS. Specifically, we connect four contributions. First, we compare two frameworks for for adaptive importance sampling (AIS) tailored to SNIS. The former exploits the view of SNIS as a ratio of two UIS estimators, coupling two separate AIS samplers in an extended-space joint distribution. The latter instead proposes the first MCMC-driven AIS sampler directly targeting the (often overlooked) optimal SNIS proposal. Second, we establish a close connection between the optimal SNIS proposal and so-called subtractive mixture models (SMMs), where negative coefficients are possible - motivating the study of the properties of the first IS estimators using SMMs. Finally, we propose new Monte Carlo diagnostics specifically for SNIS. They extend existing diagnostics for numerator and denominator by incorporating their statistical dependence, drawing on different notions of tail dependence from multivariate extreme value theory.

Bowen Fang (University of Warwick) - Splitting schemes and parameter inference in univariate stochastic differential equations with Holder diffusion coefficients
Many real-world biological phenomena, such as population dynamics, neuronal activity, and ecological systems, are modeled using stochastic differential equations (SDEs) with multiplicative noise. Important one-dimensional examples include the Jacobi (Wright-Fisher) processes for genetic drift and neuronal models, as well as the broader Pearson diffusion class, the stochastic Ginzburg-Landau equation, and the stochastic Verhulst equation. However, exact simulation schemes for these models are often un-available or computationally prohibitive. In this work, we propose a novel numerical scheme for univariate SDEs with locally Lipschitz drift and Hölder continuous diffusion coefficients, and prove its mean-square convergence. Differently from other existing results based on the Lamperti transform, our approach belongs to the class of splitting schemes. Specifically, we decompose the original equation into explicitly solvable subequations, and then compose their solutions with two compositions schemes. The derived scheme yields notable properties on the numerical and inferential side. With respect to the former, it outperforms traditional stochastic Taylor expansion methods, such as Euler-Maruyama, in both order of con-vergence and property preservation. For example, it ensures boundary preservation for SDEs with constrained state spaces and improves empirical distribution convergence to invariant measures, allowing for more accurate and robust simulations. Beyond simulation, these splitting schemes admit tractable transition densities, en-abling parameter inference via pseudo-maximum likelihood estimation and Bayesian approaches, providing a practical framework for learning parameters of interest in com-plex biological systems.

Shu Huang (University of Warwick) - Inference for Diffusion Processes via Controlled Sequential Monte and splitting schemes
We introduce an inferential framework for a wide class of semi-linear stochastic differential equations (SDEs) with additive noise, with drift satisfying a global one-sided Lipschitz condition with at most polynomial growth. Recently, explicit mean-square convergent numerical splitting schemes have been shown to 1) preserve important structural properties of the SDE (e.g. hypoellipticity in every iteration step, geometric ergodicity, oscillatory dynamics); 2) give rise to explicit pseudo-likelihoods for fully observed processes. Here, under different observation regimes and SDEs (e.g. partially observed, hypoelliptic, fully observed with additive noise), we formalise the computation of the implied pseudo-likelihoods as the normalizing constant of a Feynman-Kac flow, allowing its efficient estimation by the controlled Sequential Monte Carlo algorithm. The estimated pseudo-likelihood is then used within a pseudo-likelihood-driven Markov chain Monte Carlo method to target the posterior distribution in the Bayesian framework, and numerically optimised to obtain point estimates that enjoys good asymptotic properties at relatively low computational cost in the frequentist settings. We will illustrate our method on the partially observed hypoelliptic FitzHugh-Nagumo model, whose first component, the only observed, describes the membrane voltage evolution of a single neuron. Our simulation results show that the proposed approach achieves low variance with a bias that can be corrected via bridge sampling.

David Huk (University of Warwick) - Your copula is a classifier in disguise: classification-based copula density estimation
We propose reinterpreting copula density estimation as a discriminative task. Under this novel estimation scheme, we train a classifier to distinguish samples from the joint density from those of the product of independent marginals, recovering the copula density in the process. We derive equivalences between well-known copula classes and classification problems naturally arising in our interpretation. Furthermore, we show our estimator achieves theoretical guarantees akin to maximum likelihood estimation. By identifying a connection with density ratio estimation, we benefit from the rich literature and models available for such problems. Empirically, we demonstrate the applicability of our approach by estimating copulas of real and high-dimensional datasets, outperforming competing copula estimators in density evaluation as well as sampling.

Dr Maria Sudell (University of Liverpool) - Joint or simultaneous modelling of related longitudinal and time-to-event data for a network of treatments across multiple data sources
Longitudinal data is recorded repeatedly over time, allowing trends over time to examined as well as results at a particular timepoint (examples include monthly blood pressure measurements, repeated laboratory measurements or regular mental health assessments). Time-to-event or survival data records the time until an individual experiences a clinical event of interest or withdraws from the dataset for unrelated reasons (for example time until first stroke, or time until hospital discharge). Commonly in healthcare data, related longitudinal and time-to-event data exists (for example, blood pressure measured repeatedly over time might be related in some way or predictive of time to first stroke). Ignoring this relationship could lead to misleading or biased results in analyses, so joint models that simultaneously evaluate the longitudinal and time-to-event outcomes and their relationship are useful.
In healthcare, many treatments may exist for a particular condition, for a given group of patients (a population). To make properly informed decisions about how these treatments compare to each other, we need to be able to compare them simultaneously. This can be difficult, if different data sources only involve a subset of the possible treatments (for example, if many clinical trials have been conducted for a given condition, but they each examine subsets of the possible treatments).
Network Meta Analysis (NMA) provides an approach to pool data from multiple trials, each of which compare a subset of treatments from the complete set of possible treatments for a population (as long as a connected "network" of treatments can be drawn from the available data). Approaches for separate longitudinal NMA and separate time-to-event NMA currently exist, but not for NMA involving both longitudinal and time-to-event data. This research provides novel methodology and code linking joint modelling with NMA approaches, to better allow evaluation of all available treatment options and their effects on longitudinal and time-to-event outcomes of interest.
The proposed methodology and code is applied to a multi-study cardiovascular dataset, containing repeated blood pressure measurements, and the times until various cardiovascular events (stroke, myocardial infarction, death), for a network of anti-hypertensive treatments.

Jixin Wang (Imperial College London) - Revisiting a Theorem of JP Kahane on Random Covering in R^d
Let ${\cal{C}}$ be a $d$-dimensional convex set of unit volume and assume that the numbers $1 > l_1 \ge l_2 \ge \ldots$ are given. Let ${\mathbb{T}^d}$ denote the $d$-dimensional torus of unit volume and equal sides (the $d$ unit cube with opposite faces identified) and let ${\bf{z}}_1,{\bf{z}}_2,\ldots$ be I.I.D. uniform points in ${\mathbb{T}^d}$. Further, let ${\bf{z}}_n \oplus (l_n \ast {\cal{C}})$ be a rescaled version of ${\cal{C}}$ {\em with volume} $l_n$ translated to $\bf{z}_n$. In this paper, we prove a necessary and sufficient condition for the union of homothetic copies ${\bf{z}}_n \oplus (l_n \ast {\cal{C}}), 1 \le n < \infty$, of ${\cal{C}}$ to cover every point of ${\mathbb{T}^d}$ infinitely often w.p. 1. This generalizes and extends a theorem of JP Kahane in \cite{kahane1990recouvrements} for a.s. covering.

Mengxin Xi (King's College London) - Extrapolation and Smoothing of Tempered Posteriors
In Bayesian computational statistics, estimating expectations with respect to the posterior distribution is often of interest. Estimation with the majority of Markov Chain Monte Calo (MCMC) algorithms can be computationally challenging when dealing with an informative posterior distribution. In these cases, sampling methods could fail to yield high-quality samples under limited computational budgets. A well-known approach addressing these issues for exploring full state space of complex distributions is tempering. In most approaches based on tempering, significant computational resources are devoted to sampling from the complex, untempered posterior p1, and quantities of interest are approximated using the obtained samples accordingly. This work focuses on methods for approximating intractable Bayesian posterior quantities of interest using tempered distributions. In paticular, our contribution reveals that approximating p1 may be unnecessary, as posterior quantities of interest can, in principle, be extrapolated based on their tempered equivalents with t < 1.