140 citations · 1.9k across the 86 of their papers we have counts for
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Optimizing The Integrator Step Size for Hamiltonian Monte Carlo
M. J. Betancourt, Simon Byrne, Mark Girolami
Hamiltonian Monte Carlo can provide powerful inference in complex statistical problems, but ultimately its performance is sensitive to various tuning parameters. In this paper we u…
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…
Control functionals for Monte Carlo integration
Chris J. Oates, Mark Girolami, Nicolas Chopin
A non-parametric extension of control variates is presented. These leverage gradient information on the sampling density to achieve substantial variance reduction. It is not requir…
Solving Large-Scale PDE-constrained Bayesian Inverse Problems with Riemann Manifold Hamiltonian Monte Carlo
Tan Bui-Thanh, Mark Girolami
We consider the Riemann manifold Hamiltonian Monte Carlo (RMHMC) method for solving statistical inverse problems governed by partial differential equations (PDEs). The power of the…
The Controlled Thermodynamic Integral for Bayesian Model Comparison
Chris J. Oates, Theodore Papamarkou, Mark Girolami
Bayesian model comparison relies upon the model evidence, yet for many models of interest the model evidence is unavailable in closed form and must be approximated. Many of the est…
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…