104 citations · 324 across the 15 of their papers we have counts for
17 papers
High-dimensional Adaptive MCMC with Reduced Computational Complexity
Max Hird, Samuel Livingstone
We propose an adaptive MCMC method that learns a linear preconditioner which is dense in its off-diagonal elements but sparse in its parametrisation. Due to this sparsity, we achie…
A note on diffusive/random-walk behaviour in Metropolis--Hastings algorithms
Yuxin Liu, Peiyi Zhou, Samuel Livingstone
We prove a general result that if a Metropolis--Hastings algorithm has a proposal that is not geometrically ergodic and the acceptance rate approaches unity at a suitable rate as t…
Adaptive MCMC for Bayesian variable selection in generalised linear models and survival models
Xitong Liang, Samuel Livingstone, Jim Griffin
Developing an efficient computational scheme for high-dimensional Bayesian variable selection in generalised linear models and survival models has always been a challenging problem…
Sampling algorithms in statistical physics: a guide for statistics and machine learning
Michael F. Faulkner, Samuel Livingstone
We discuss several algorithms for sampling from unnormalized probability distributions in statistical physics, but using the language of statistics and machine learning. We provide…
Optimal design of the Barker proposal and other locally-balanced Metropolis-Hastings algorithms
Jure Vogrinc, Samuel Livingstone, Giacomo Zanella
We study the class of first-order locally-balanced Metropolis--Hastings algorithms introduced in Livingstone & Zanella (2021). To choose a specific algorithm within the class the u…
Adaptive random neighbourhood informed Markov chain Monte Carlo for high-dimensional Bayesian variable Selection
Xitong Liang, Samuel Livingstone, Jim Griffin
We introduce a framework for efficient Markov Chain Monte Carlo (MCMC) algorithms targeting discrete-valued high-dimensional distributions, such as posterior distributions in Bayes…
A general perspective on the Metropolis-Hastings kernel
Christophe Andrieu, Anthony Lee, Sam Livingstone
Since its inception the Metropolis-Hastings kernel has been applied in sophisticated ways to address ever more challenging and diverse sampling problems. Its success stems from the…
A fresh take on 'Barker dynamics' for MCMC
Max Hird, Samuel Livingstone, Giacomo Zanella
We study a recently introduced gradient-based Markov chain Monte Carlo method based on 'Barker dynamics'. We provide a full derivation of the method from first principles, placing…
The Barker proposal: combining robustness and efficiency in gradient-based MCMC
Samuel Livingstone, Giacomo Zanella
There is a tension between robustness and efficiency when designing Markov chain Monte Carlo (MCMC) sampling algorithms. Here we focus on robustness with respect to tuning paramete…
Peskun-Tierney ordering for Markov chain and process Monte Carlo: beyond the reversible scenario
Christophe Andrieu, Samuel Livingstone
Historically time-reversibility of the transitions or processes underpinning Markov chain Monte Carlo methods (MCMC) has played a key rôle in their development, while the self-adjo…
Kinetic energy choice in Hamiltonian/hybrid Monte Carlo
Samuel Livingstone, Michael F. Faulkner, Gareth O. Roberts
We consider how different choices of kinetic energy in Hamiltonian Monte Carlo affect algorithm performance. To this end, we introduce two quantities which can be easily evaluated,…
On the Geometric Ergodicity of Hamiltonian Monte Carlo
Samuel Livingstone, Michael Betancourt, Simon Byrne +1
We establish general conditions under which Markov chains produced by the Hamiltonian Monte Carlo method will and will not be geometrically ergodic. We consider implementations wit…
Geometric ergodicity of the Random Walk Metropolis with position-dependent proposal covariance
Samuel Livingstone
We consider a Metropolis--Hastings method with proposal , where is the current state, and study its ergodicity properties. We show that suitable cho…
Gradient-free Hamiltonian Monte Carlo with Efficient Kernel Exponential Families
Heiko Strathmann, Dino Sejdinovic, Samuel Livingstone +2
We propose Kernel Hamiltonian Monte Carlo (KMC), a gradient-free adaptive MCMC algorithm based on Hamiltonian Monte Carlo (HMC). On target densities where classical HMC is not an o…
The Geometric Foundations of Hamiltonian Monte Carlo
M. J. Betancourt, Simon Byrne, Samuel Livingstone +1
Although Hamiltonian Monte Carlo has proven an empirical success, the lack of a rigorous theoretical understanding of the algorithm has in many ways impeded both principled develop…
Information-geometric Markov Chain Monte Carlo methods using Diffusions
Samuel Livingstone, Mark Girolami
Recent work incorporating geometric ideas in Markov chain Monte Carlo is reviewed in order to highlight these advances and their possible application in a range of domains beyond S…
Langevin diffusions and the Metropolis-adjusted Langevin algorithm
Tatiana Xifara, Chris Sherlock, Samuel Livingstone +2
We provide a clarification of the description of Langevin diffusions on Riemannian manifolds and of the measure underlying the invariant density. As a result we propose a new posit…