PCM LECTURES 2025-26

Prof. Gareth Roberts

University of Warwick, Dept of Statistics University of Warwick Coventry CV4 7AL,United Kingdom

PROFILE

Speaker Bio

Tentative schedule is given below. Final schedule and details will be updated in January

COLLOQUIUM 1

Title:	Retrospective stochastic simulation
Date:	13 February 2026 (FRIDAY) Time: 2.30 PM-3.30 PM
Venue:	TBA
Abstract:	The stochastic simulation toolkit consists of many versatile and powerful techniques beginning with the elementary rejection and importance sampling, through Markov chain Monte Carlo and Sequential Monte Carlo methods, and through to ever more sophisticated methods such as particle MCMC and Hamiltonian methods. Although incredibly successful, these methods can often be computationally very expensive to implement. This talk will introduce "Retrospective Simulation" methods. Compared to the usual sequential constructions suggested by these methods' mathematical constructions, these methods offer simple but often dramatically successful improvements to these methods by judicious changes in the order of simulation steps. The methods will be illustrated using a range of examples.

COLLOQUIUM 2

Title:	Piecewise-deterministic Markov processes and principled subsampling for Bayesian inference
Date:	13 February 2026 (FRIDAY) Time: 4.00 PM-5.00 PM
Venue:	TBA
Abstract:	Traditional Markov chain Monte Carlo (MCMC) methods almost always rely on the Metropolis-Hastings mechanism, thereby constructing a reversible Markov chain. However in recent years non-reversible MCMC methods have emerged as viable alternatives with distinct advantages compared to reversible methods. From a practical perspective, perhaps the most promising class of such algorithms are those constructed from Piecewise-deterministic Markov processes (PDMPs). This lecture will review these methods and discuss their convergence properties and practical implementation. The presentation will consider subsampling strategies, which enable algorithms to be implemented for large data problems without the expensive computational cost of evaluating the likelihood at each iteration. In contrast to diffusion-motivated algorithms, one important advantage of PDMP methods is that subsampling methods can be implemented without biasing the resulting invariant distribution. For illustration, most attention will be devoted to the Zig-Zag algorithm although the presentation will also discuss the Bouncy Particle Sampler and its stereographic alternative.

PUBLIC LECTURE

Title:	Biases in draws for major football competitions, and how to fix them
Date:	TBA
Venue:	TBA



Abstract:	Draws for major sporting events are often televised and carried out in a sequential fashion to maximise excitement and to increase anticipation for the sporting event itself. In this regard, organisations such as FIFA and UEFA in football have been highly successful. However these draw procedures are also often subject to constraints which make the problem of simulating a fair draw (ie uniform over all feasible draws which satisfy the constraints) difficult to achieve using a sequential procedure. For example the recent FIFA World Cup draw imposed geographical constraints to avoid countries from the same continental confederation (apart from Europe) playing each other in the group stages. Recent draws by FIFA and UEFA have all (to a greater or lesser extent) been biased. This talk will investigate these biases and suggest practical solutions which respect the desire to unveil such a draw in a sequential fashion. The algorithms developed will be examples of a class of algorithms known as Retrospective Simulation. The main focus will be on the FIFA 2022 World Cup draw. This is joint work with Jeffrey Rosenthal.

COLLOQUIUM

Title:	Ballistic Markov chain Monte Carlo and the scaling problem
Date:	TBA
Venue:	TBA



Abstract:	Markov chain Monte Carlo algorithms are traditionally constructed as reversible Markov chains. One disadvantage they frequently suffer from is so-called "random walk behaviour" whereby moves in a particular direction are cancelled out by subsequent moves in the reverse direction leading to overall slow mixing. Improvements result from chains with momentum which reduces random walk-behaviour producing "ballistic" rather than "diffusive" Markov chain trajectories. 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. The presentation will investigate how these behave in a collection of stylised high-dimensional examples showing that the non-reversibility can often be lost in the high-dimensional limit when algorithm scale parameters are chosen to optimise mixing. On the other hand, lifted algorithms still retain a uniform efficiency advantage over their reversible counterparts. The results will be applied to the "simulated tempering" algorithm.

COLLOQUIUM 1

Title:	Retrospective stochastic simulation
Date:	23 February 2026 (MONDAY) Time: 2.15 PM-3.15 PM
Venue:	Auditorium (II floor)

Abstract:	The stochastic simulation toolkit consists of many versatile and powerful techniques beginning with the elementary rejection and importance sampling, through Markov chain Monte Carlo and Sequential Monte Carlo methods, and through to ever more sophisticated methods such as particle MCMC and Hamiltonian methods. Although incredibly successful, these methods can often be computationally very expensive to implement. This talk will introduce "Retrospective Simulation" methods. Compared to the usual sequential constructions suggested by these methods' mathematical constructions, these methods offer simple but often dramatically successful improvements to these methods by judicious changes in the order of simulation steps. The methods will be illustrated using a range of examples.

COLLOQUIUM 2

Title:	Exact retrospective simulation of diffusions
Date:	23 February 2026 (MONDAY) Time: 3.30 PM-4.30 PM
Venue:	TBA

Abstract:	Computational simulation of diffusion sample paths in general requires appropriate time-discretisation schemes, the simplest of which is the Euler-Maruyama approach. Although these schemes can be effective and are underpinned by theoretical guarantees to control statistical biases caused by the discretisation. These biases can be rendered arbitrarily small using increasingly fine mesh size, although this comes at a cost of increased computational burden. However retrospective simulation methods can provide algorithms to simulate from certain classes of diffusions without the need to resort to discretisations. This presentation will introduce these methods and show that they can be highly efficient as well as unbiased. These methods can be applied to any class of diffusions with constant diffusion coefficient and with drift of gradient form. The final part of the talk will introduce importance sampling alternatives which can be used to relax these stringent conditions.