I consider the development of Markov chain Monte Carlo (MCMC) methods, from late-1980s
Gibbs sampling to present-day gradient-based methods and piecewise-deterministic Markov …

In this paper, we focus on numerical approximations of Piecewise Diffusion Markov
Processes (PDifMPs), particularly when the explicit flow maps are unavailable. Our …

Abstract Novel Monte Carlo methods to generate samples from a target distribution, such as
a posterior from a Bayesian analysis, have rapidly expanded in the past decade. Algorithms …

We introduce a novel class of generative models based on piecewise deterministic Markov
processes (PDMPs), a family of non-diffusive stochastic processes consisting of …

We introduce the Velocity Jumps approach, denoted as JUMP, a new class of Molecular
dynamics integrators, replacing the Langevin dynamics by a hybrid model combining a …

Markov chain Monte Carlo (MCMC) is a key algorithm in computational statistics, and as
datasets grow larger and models grow more complex, many popular MCMC algorithms …

Motivated by applications to mathematical biology, we study the averaging problem for slow–
fast systems, in the case in which the fast dynamics is a stochastic process with multiple …

Abstract Markov chain Monte Carlo (MCMC) is a key algorithm in computational statistics,
and as datasets grow larger and models grow more complex, many popular MCMC …

In this thesis, we study discretizations of kinetic Langevin dynamics within the context of
Markov chain Monte Carlo. We compare the convergence properties for different choices of …

We introduce novel Markov chain Monte Carlo (MCMC) algorithms based on numerical
approximations of piecewise-deterministic Markov processes obtained with the framework of …