Centre for Computational Statistics and Machine Learning

The Metropolis-adjusted Langevin algorithm (MALA) and manifold-variant (MMALA) are two Markov chain Monte Carlo methods based on diffusions. While theoretical properties of the former are better understood, the latter has appeared more effective in practice, producing more efficient estimates for the same computational budget in many experiments (e.g. Girolami & Calderhead, 2011). The focus of this talk will be to highlight two properties of the diffusion on which MMALA is based, which suggest that a slightly different diffusion would prove a better basis for MCMC, both in terms of proposal choice and speed of computation.

The talk will be in two parts. In the first half I’ll review the motivation for diffusion-based MCMC methods like MALA, and use this motivation to derive a diffusion with position-dependent volatility which would seem to be a good choice in this respect. After this I’ll highlight why the diffusion on which previous position-dependent Langevin algorithms (such as MMALA and a similar algorithm suggested in Roberts & Stramer, 2002) are based is different to this, which involve introducing some simple concepts from differential geometry. To add some weight to the claim that the new algorithm is in fact a more suitable choice for MCMC, I’ll then show some experimental results from a range of statistical models.

This is joint work with Chris Sherlock & Tatiana Xifara (Lancaster), and Simon Byrne & Mark Girolami (UCL).

Slides for the talk: PDF