This workshop will focus on the methodological and theoretical foundations of Markov Chain Monte Carlo (MCMC) methods, which are central to modern computational statistics, Bayesian inference, and a broad range of applications in physics, engineering, and data science. MCMC algorithms enable sampling from complex, high-dimensional probability distributions and are indispensable in situations where direct analytic or deterministic computational methods fail.

In recent years, the field has seen rapid developments aimed at improving the efficiency and robustness of MCMC techniques. These include advances in sampling from high-dimensional spaces, dealing with multimodal or non-smooth target distributions, and understanding the convergence properties and computational complexity of various algorithms. Such challenges are critical in emerging applications across machine learning, inverse problems, and computational physics.

The goal of the workshop is to bring together leading international experts as well as early-career researchers working at the forefront of MCMC methodology. By fostering discussion and exchange of ideas, the workshop aims to advance understanding of fundamental issues, stimulate new collaborations, and identify promising directions for future research. The program will include invited talks, contributed presentations, and ample time for informal interaction, with the intent of nurturing a dynamic and inclusive research community around MCMC methods.

Organisers

Joris Bierkens	TU Delft
Blazej Miasojedow	University of Warsaw

Speakers

Christophe Andrieu	University of Bristol	abstract
Nicolas Chopin	ENSAE, Institut Polytechnique de Paris	abstract
Andreas Eberle	University of Bonn	abstract
Krzysztof Łatuszyński	University of Warwick
Samuel Livingstone	University College London	abstract
Frank van der Meulen	Vrije Universiteit Amsterdam	abstract
Eric Moulines	Ecole Polytechnique	abstract
Marcelo Pereyra	Heriot-Watt University	abstract
Gareth Roberts	University of Warwick	abstract
Katharina Schuh	TU Wien	abstract
Dootika Vats	Indian Institute of Technology Kanpur	abstract
Matti Vihola	University of Jyväskylä	abstract
Marija Vucelja	University of Virginia	abstract
Giacomo Zanella	Bocconi University	abstract

Programme

Wednesday 10 December 2025
10:00-10:30	Welcome and registration
10:30-10:40	Opening
10:40-11:30	Dootika Vats
11:30-12:20	Sam Livingstone
12:20-13:30	Lunch
13:30-14:20	Giacomo Zanella
14:20-15:10	Andreas Eberle
15:10-15:40	Break
15:40-16:30	Gareth Roberts
16:30-18:00	Poster session and reception
Thursday 11 December 2025
9:00-9:30	Welcome and coffee
9:30-10:20	Katharina Schuh
10:20-10:50	Break
10:50-11:40	Marcelo Pereyra
11:40-12:30	Marija Vucelja
12:30-13:45	Lunch
13:45-14:35	Frank van der Meulen
14:35-15:25	Nicholas Chopin
15:25-15:55	Break
15:55-16:45	Matti Vihola
18:00	Conference dinner
Friday 12 December 2025
9:00-9:30	Welcome and coffee
9:30-10:20	Christophe Andrieu
10:20-10:50	Break
10:50-11:40	Eric Moulines
11:40-12:30	Krzysztof Łatuszyński
12:30-12:35	Closing
12:35-14:00	(Take-away) Lunch

Registration

The workshop is fully booked, and registration is no longer possible.
If you would like to be placed on the waiting list, please send an email to eurandom.office@tue.nl.

 

Abstracts

Christophe Andrieu

Gradient-free optimization via integration
We develop and analyse an approach to optimize functions $l\colon \mathbb{R}^d\rightarrow \mathbb{R}$ not assumed to be convex, differentiable or even continuous. The algorithm belongs to the class of model-based search methods. The idea is to fit recursively $l$ to a parametric family of distributions, using a Bayesian update followed by a reprojection back onto the chosen family. Remarkably, reprojection in our scenario boils down to computing expectations, which can be simply approximated through Monte Carlo. We show that when the family of distributions is appropriately chosen this approach can be interpreted as an implicit time-inhomogeneous gradient descent algorithm on a sequence of smoothed approximations of $l$, providing a route to establishing convergence. We establish new results for generic inhomogeneous gradient descent algorithms, which we specialise to the model-based search algorithm in the Gaussian scenario. We illustrate the performance of the algorithm on a challenging classification task in machine learning.

joint work with Nicolas Chopin, Ettore Fincato and Mathieu Gerber ( https://arxiv.org/abs/2408.00888).

 

Nicolas Chopin

What is actual the complexity of tempering (SMC) ? 
There is some discrepancy in the literature regarding the complexity of tempering with respect to d, the dimension of the sampling space. The complexity is partly determined by the length of the temperature ladder, that is, the sequence of tempering exponents 0=lambda_0 < … < lambda_T = 1. In the AIS (annealed importance sampling) literature, it is often recommended to take T = O(d). Some SMC (Sequential Monte Carlo) papers instead suggest that ESS-based criteria leads to T=O(d^{1/2}).
In this talk, I will present results from both a recent paper (with Francesca Crucinio and Anna Korba, ICML 2024) and some preliminary work (with Yvann Le Fay and Matti Vihola) that shed light on this discrepancy. Basically, for moments with respect to the target distribution, T=O(d^{1/2})$ suffices to leads to estimates with variance O(1). However, for the normalising constant, variance is then O(T) = O(d^{1/2})$.
The actual complexity of the considered sampler will also depend, of course, on the mixing properties of the MCMC kernels used to rejuvenate the particles. I will explain how we can exploit some existing, non-asymptotic results on such kernels to obtain the overall complexity of the sampler.

 

Andreas Eberle

Event Chain Monte Carlo, self-repellent random walks, and the stochastic
heat equation
The Event Chain Monte Carlo algorithm is an MCMC method for sampling equilibrium configurations of interacting particles. When applied to a harmonic chain of oscillators, it is closely related to the self-repellent random walk on a discrete circle. We show that these processes are second order lifts of a discrete stochastic heat equation with additive noise. As a consequence, we obtain a lower bound on the relaxation times of order n^{3/2}. Moreover, we show that when the active particle is resampled with an appropriate rate, then the relaxation time has an upper bound of order n^2. On the same model, optimally tuned Hamiltonian Monte Carlo achieves a relaxation time of order n^{5/4}, but due to the gradient evaluations, its complexity is of order n^{9/4}. This confirms a conjecture of Werner Krauth that on this specific model, ECMC can outperform HMC.

This is joint work with Francis Lörler.

 

Samuel Livingstone

New preconditioning theory and methodology for MCMC sampling algorithms
I will discuss two pieces of work. In the first we present theoretical results related to preconditioning Markov chain Monte Carlo sampling algorithms. Preconditioning is a widely used technique that is known empirically to improve the mixing of Markov chain algorithms, but little has been said theoretically about it. I will present some recent work establishing some positive and negative theoretical results. I will then discuss some methodological work devising new preconditioners. The standard options to choose from in common software packages are ‘diagonal’ or ‘dense’. We will present a new alternative option that seeks to improve upon diagonal preconditioning whilst also being less computationally expensive than the quadratic cost required for the dense option.

Both projects are joint work with my former PhD student Max Hird, now a PDRA at University of Waterloo. The first is associated with this paper: https://www.jmlr.org/papers/v26/23-1633.html.

 

Frank van der Meulen

MCMC for stochastic phylogenetic shape models
I will present a Bayesian framework for inferring a stochastic phylogenetic shape model defined on a directed tree. Although observations are limited to leaf vertices, the method simultaneously estimates the model’s unknown parameters and reconstructs ancestral shapes.
The core computational challenge is conditioning a high-dimensional diffusion process on a tree topology. I propose a general solution to this problem and outline several open questions. This approach enables stochastic character mapping directly on landmark configurations, offering a principled way to model the evolution of complex shapes while preserving their intrinsic geometric structure.

Joint work with Sofia Stroustrup, Morten Akhoj Pedersen, Stefan Sommer, Rasmus Nielsen

 

Eric Moulines

Bridging Diffusion Posterior Sampling and Monte Carlo Methods
Diffusion models have emerged as powerful generative priors for high-dimensional inference tasks, enabling realistic sample generation in imaging, physics, and biology. Recent developments exploit these models as flexible Bayesian priors to solve inverse problems without retraining. This talk surveys the growing family of diffusion posterior sampling (DPS) algorithms and reveals their deep connections with classical Monte Carlo inference. We show that many existing approaches—gradient guidance, Sequential Monte Carlo, Langevin, and variational diffusion samplers—can all be viewed as instances of a single principle: twisting the intermediate distributions of the diffusion process to align the denoising dynamics with the Bayesian posterior. Within this unified perspective, diffusion guidance appears as a soft-constrained optimal-transport correction that bridges learned priors and data-driven likelihoods. We discuss algorithmic implications, highlight new variants such as mixture-guided and midpoint-guided diffusion sampling, and compare their trade-offs between accuracy and computational efficiency. The presentation concludes with open challenges—scalability, bias control, and uncertainty quantification—pointing toward a principled synthesis of diffusion modeling and Monte Carlo methodology for general inverse problems.

 

Marcelo Pereyra

Fast, modular and explainable generative AI for image restoration: a distillation and Langevin sampling approach.
This talk introduces a novel mathematical and computational paradigm for developing Bayesian image restoration methods based on generative denoising diffusion models. A central innovation is our use of Langevin diffusion processes and MCMC sampling techniques to create highly flexible and accurate stochastic neural network architectures for Bayesian imaging. These stochastic networks are built from clear, interpretable layers that model statistical image priors and data likelihood functions, derived from a discrete-time approximation of a Langevin diffusion processes. The data likelihood layers are particularly flexible, allowing instrumental and degradation models to be defined at inference time and seamlessly combined with pre-trained image priors derived from generative AI models. To significantly enhance computational efficiency, we employ adversarial model distillation, which allows us to achieve excellent results with as few as 8 neural function evaluations. We validate our approach through extensive experiments and compare it with alternative methods from the state of the art.

The material for this talk is drawn from our recent work on generative AI for Bayesian image restoration, namely https://arxiv.org/abs/2503.12615 that utilises a distilled latent Stable Diffusion XL image-text model in a zero-shot manner, and https://arxiv.org/pdf/2507.02686 which combines pre-trained pixel-based diffusion models with deep unfolding and diffusion distillation techniques.

 

Gareth Roberts

Ballistic and diffusive lifted MCMC, with application to parallel tempering
In this talk I will review the popular “lifting” mechanism for producing non-reversible Markov chain Monte Carlo such as non-reversible Metropolis-Hastings and piecewise-deterministic Markov processes. These methods aim to have better mixing by providing momentum to break down random walk behaviour of algorithms.The presentation will investigate how these behave in a collection of stylised high-dimensional examples showing that the non-reversibility can often be washed out by the problem complexity so that the algorithm behaves asymptotically in a reversible way. On the other hand lifted algorithms still retain a small efficiency advantage over their reversible counterparts. Furthermore, we will show that some carefully constructed higher-order lifted Metropolis-Hastings algorithms can retain some aspects of ballistic behaviour, even in the high-dimensional limit setting.

 

Katharina Schuh

Convergence of kinetic Langevin samplers for non-convex potentials
In this talk we study three kinetic Langevin samplers: the Euler discretization of the kinetic Langevin dynamics, the BU splitting scheme, and the UBU splitting scheme. We focus on their efficiency in sampling a given probability distribution in R^d with non-convex potential. We show contraction results in L^1-Wasserstein distance for all three samplers. These results are based on a carefully tailored distance function and an appropriate coupling construction. Additionally, we analyse the error in the L^1-Wasserstein distance between the target measure and the invariant measure of the discretization scheme. To get an ε-accuracy in L^1-Wasserstein distance, we show complexity guarantees of order O(d^(1/2)/ε) for the Euler scheme and O(d ^(1/4)/ε) for the UBU scheme under appropriate assumptions on the target measure. These results extend to interacting particle systems and provide bounds for sampling mean-field type probability measures. The talk is based on joint work with Peter A. Whalley.

 

Dootika Vats

Exact MCMC for Intractable Proposals
Accept-reject based Markov chain Monte Carlo (MCMC) methods are the workhorse algorithm for Bayesian inference. These algorithms, like Metropolis-Hastings, require the choice of a proposal distribution which is typically informed by the desired target distribution. Surprisingly, proposal distributions with unknown normalizing constants are not uncommon, even though for such a choice of a proposal, the Metropolis-Hastings acceptance ratio cannot be evaluated exactly. Across the literature, authors resort to approximation methods that yield inexact MCMC or develop specialized algorithms to combat this problem. We show how Bernoulli factory MCMC algorithms, originally proposed for doubly intractable target distributions, can quite naturally be adapted to this situation. We present diverse and relevant examples demonstrating the usefulness of the Bernoulli factory approach to this problem.

 

Matti Vihola

Mixing time of the conditional backward sampling particle filter
The conditional backward sampling particle filter (CBPF; also known as the particle Gibbs with ancestor sampling, PGAS) is a powerful Markov chain Monte Carlo sampler for general state space hidden Markov model smoothing. It was proposed as an improvement over the conditional particle filter, which is known to have an O(T^2) computational time complexity under a general `strong’ mixing assumption, where T is the time horizon. We provide the first proof that the CBPF admits an O(T log T) time complexity under strong mixing, complementing strong empirical evidence of the superiority of the CBPF in practice. In particular, the CBPF’s mixing time is upper bounded by O(log T), for any sufficiently large number of particles N that depends only on the mixing constants and not T. We show that an O(log T) mixing time is optimal. The proof involves the analysis of a novel coupling of two CBPFs, which involves a maximal coupling of two particle systems at each time instant. The coupling is implementable, and thus can also be used to construct unbiased, finite variance, estimates of functionals which have arbitrary dependence on the latent state’s path, with a total expected cost of O(Tlog T).

The talk is based on the joint work with Joona Karjalainen, Sumeetpal S. Singh, and Anthony Lee: [2312.17572] Mixing time of the conditional backward sampling particle filter

Marija Vucelja

Thermal Relaxation on Random Graphs via Metropolis and Glauber Dynamics
Efficient sampling algorithms rely on dynamics that drive a physical system rapidly toward its target state. I will introduce the Mpemba effect—an anomalous thermal relaxation phenomenon in which a system initially at a higher temperature cools down more quickly than one starting at a lower temperature—and its heating analog, in which a cooler initial state can lead to faster heating than a hotter initial state. We investigate thermal relaxation in quenched disordered systems under Metropolis and Glauber dynamics, examining how varying transition rates affects relaxation behavior. We show that Metropolis dynamics on a complete graph cannot exhibit the Mpemba effect, whereas on an incomplete graph it can. Even rank-one perturbations of the transition rates are sufficient to generate anomalous relaxation. Finally, we discuss the probability of observing the Mpemba effect in the large-temperature limit.

Giacomo Zanella

A fast non-reversible sampler for Bayesian finite mixture models
Finite mixtures are a cornerstone of Bayesian modelling, and it is well-known that sampling from the resulting posterior distribution can be a hard task. In particular, popular reversible Markov chain Monte Carlo schemes are often slow to converge when the number of observations n is large. In this paper we introduce a novel and simple non-reversible sampling scheme for Bayesian finite mixture models, which is shown to drastically outperform classical samplers in many scenarios of interest, especially during convergence phase and when components in the mixture have non-negligible overlap. At the theoretical level, we show that the performance of the proposed non-reversible scheme cannot be worse than the standard one, in terms of asymptotic variance, by more than a factor of four; and we provide a scaling limit analysis suggesting that the non-reversible sampler can reduce the convergence time from O(n^2) to O(n). We also discuss why the statistical features of mixture models make them an ideal case for the use of non-reversible discrete samplers.

 

Sponsors

This workshop is sponsored by