Richard Everitt | Sequential Monte Carlo and Active Subspaces

Speaker: Dr. Richard Everitt (University of Warwick)

Date: 8th Sep 2025 - 14:00 to 14:25

Title: Sequential Monte Carlo and Active Subspaces.

Event: Workshop on non-reversible Sampling | Robustness-Methodology-Applications

Abstract: Constantine et al. (2016) introduced a Metropolis-Hastings (MH) approach that target the active subspace of a posterior distribution: a linearly projected subspace that is informed by the likelihood.. Schuster et al. (2017) refined this approach to introduce a pseudo-marginal Metropolis-Hastings, integrating out inactive variables through estimating a marginal likelihood at every MH iteration. In this talk we show empirically that the effectiveness of these approaches is limited in the case where the linearity assumption is violated, and suggest a particle marginal Metropolis-Hastings algorithm as an alternative for this situation. The high computational cost of these approaches leads us to consider alternative approaches to using active subspaces in MCMC that avoid the need to estimate a marginal likelihood: we introduce Metropolis-within-Gibbs and Metropolis-within-particle Gibbs methods that provide a more computationally efficient use of the active subspace.
This is joint work with Leonardo Ripoli (Reading).

Paper at https://arxiv.org/abs/2501.05144

Constantine, P.G., C. Kent, and T. Bui-Thanh. 2016. Accelerating Markov Chain Monte Carlo withActive Subspaces. SIAM Journal on Scientific Computing 38(5): A2779–A2805. https://doi.org/10.1137/15M1042127
Schuster, I., P.G. Constantine, and T.J. Sullivan. 2017. Exact active subspace Metropolis-Hastings, withapplications to the Lorenz-96 system. https://arxiv.org/abs/1712.02749
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