The workshop will consist of two traditional talks, a networking session, and two interactive hands-on sessions.
The workshop will be an in-person event and will take place in Edinburgh.
The following is a tentative schedule:
Talks
2:30 - 3:00 Gonçalo Dos Reis (University of Edinburgh)
3:00 - 3:30 Olga Iziumtseva (University of Nottingham)
Networking break
3:30 - 4:00
Hands-on session
4:00 - 4:30 Abdul-Lateef Haji-Ali(Heriot Watt University)
4:30 - 5:00 Yordan Raykov (University of Nottingham)
Olga Iziumtseva (University of Nottingham)
Self-intersection local times of Volterra Gaussian processes in stochastic flows with interaction
Joint work with Wasiur R. Khudabukhsh
In this talk, we discuss the existence of multiple self-intersection local times for stochastic processes x(u(s),t), s\in [0,1], where u is a Volterra Gaussian process and
x is the solution to the equation with interaction driven by the occupation measure of the process u. It appears that self-intersection local times for the process x(u(s),t), s\in[0,1] can be defined as weighted self-intersection local times for the process u. We present conditions on Volterra Gaussian processes and weight functions sufficient for the existence of weighted self-intersection local times for a large class of unbounded weights.
Yordan Raykov (University of Nottingham)
Amortised Inference in Discrete Spaces
This tutorial will provide a practical introduction to amortized inference methods for complex discrete and structured spaces. We will begin by reviewing the motivation for amortization: replacing repeated, instance-specific optimisation or sampling with learned inference mechanisms that generalise across related problems. The main focus will be on Generative Flow Networks, which learn sequential stochastic policies for sampling discrete objects with probability proportional to a target reward. We will cover the basic mathematical formulation, connections to variational inference and reinforcement learning, and implementation details for objectives such as flow matching and trajectory balance. Examples will emphasise applications in Bayesian structure learning, combinatorial model discovery, and other settings where posterior mass is distributed across many high-quality discrete configurations.
Abdul-Lateef Haji-Ali (Heriot-Watt University)
Multilevel and Multi-Index Monte Carlo: Theory, Practice, and mimclib
This tutorial gives a focused introduction to Multilevel Monte Carlo (MLMC) and its natural extension to Multi-Index Monte Carlo (MIMC), aimed at researchers who want to go beyond standard Monte Carlo in settings with expensive hierarchical approximations. I will introduce the core ideas -- the telescoping variance reduction argument, the complexity theorem, and where classical MLMC loses optimality -- before showing how MIMC recovers this optimality by replacing first-order differences with high-order mixed differences, dramatically reducing variance across a wider class of problems.
The second half of the tutorial is hands-on, demonstrating how to use mimclib (github.com/haji-ali/mimclib), an open-source library that supports both MLMC and MIMC workflows with parallel execution, database-backed storage, and automated convergence diagnostics. Attendees will leave with a working template they can adapt to their own samplers and a clear picture of how to tune the method's key parameters in practice.
Gonçalo Dos Reis (University of Edinburgh)
Simulation of mean-field SDEs: some recent results
Abstract: We review two results in the simulation for SDE of McKean-Vlasov type (MV-SDE) with the aim of statistical applications. The first block of results addresses simulation of MV-SDEs having super-linear growth in the spatial and the interaction component in the drift, and non-constant Lipschitz diffusion coefficient. The 2nd block is far more curious. It addresses the study the weak convergence behaviour of the Leimkuhler--Matthews method, a non-Markovian Euler-type scheme with the same computational cost as the Euler scheme, for the approximation of the stationary distribution of a one-dimensional McKean--Vlasov Stochastic Differential Equation (MV-SDE). The particular class under study is known as mean-field (overdamped) Langevin equations (MFL). We provide weak and strong error results for the scheme in both finite and infinite time. We work under a strong convexity assumption. Based on a careful analysis of the variation processes and the Kolmogorov backward equation for the particle system associated with the MV-SDE, we show that the method attains a higher-order approximation accuracy in the long-time limit (of weak order convergence rate 3/2) than the standard Euler method (of weak order 1). While we use an interacting particle system (IPS) to approximate the MV-SDE, we show the convergence rate is independent of the dimension of the IPS and this includes establishing uniform-in-time decay estimates for moments of the IPS, the Kolmogorov backward equation and their derivatives. The theoretical findings are supported by numerical tests.
This presentation is based on the joint work [1], [2].
[1] Chen, X., Dos Reis, G., Stockinger, W. and Wilde, Z., 2025. Improved weak convergence for the long-time simulation of mean-field Langevin equations. Electronic Journal of Probability, 30, pp.1-81.
[2] X. Chen, G. dos Reis. "Euler simulation of interacting particle systems and McKean-Vlasov SDEs with fully superlinear growth drifts in space and interaction" IMA Journal of Numerical Analysis, 44, no. 2 (2024), 751-796.