Multigrid Monte Carlo Revisited: Theory and Bayesian Inference
Event details
| Date | 04.09.2024 |
| Hour | 16:15 › 17:15 |
| Speaker | Dr. Yoshihito Kazashi - University of Strathclyde Glasgow |
| Location | |
| Category | Conferences - Seminars |
| Event Language | English |
Abstract:
In this talk, I revisit the multigrid Monte Carlo (MGMC) method proposed by Goodman and Sokal [Goodman and Sokal, (1989) Multigrid Monte Carlo method. Conceptual foundations], a random sampler analogue of deterministic multigrid solvers.
MGMC accelerates random samplers, such as Gibbs samplers, by drawing on insights from numerical analysis. The primary focus of this talk is to provide theoretical support. We discuss a grid-size-independent convergence theory for MGMC, applicable to general Gaussian random variables. This theory demonstrates that the first two moments, which fully characterize the Gaussian distribution, converge exponentially to their target values at a uniform rate. Additionally, we examine the exponential decay of autocorrelations in the generated samples. Furthermore, we extend the application of the MGMC method to address the important scenario of sampling posterior Gaussian distributions conditioned on noisy data.
This is joint work with Eike Müller (Bath, UK) and Robert Scheichl (Heidelberg, Germany)
Practical information
- General public
- Free
Organizer
- Fabio Nobile