FLARE MCMC: Fidelity-based Layer-Adaptive REcursive proposals for MCMC

Abstract:Markov chain Monte Carlo (MCMC) requires only the ability to evaluate the likelihood, making it a common technique for inference in complex models. However, it can have a slow mixing rate, requiring the generation of many samples to obtain good estimates and an overall high computational cost. FLARE MCMC is a multi-fidelity layered MCMC method that exploits lower-fidelity approximations of the true likelihood calculation to improve mixing and leads to overall faster performance. Such lower-fidelity likelihoods are commonly available in scientific and engineering applications where the model involves a simulation whose resolution or accuracy can be tuned. Our technique uses recursive, layered chains with simple layer tuning; it does not require the likelihood to take any form or have any particular internal mathematical structure. We demonstrate experimentally that FLARE MCMC achieves larger effective sample sizes for the same computational time across different scientific domains including hydrology and cosmology.

This is the author's accepted manuscript of an article published in SIAM Journal on Uncertainty Quantification. The final version is available at \url{this https URL

Artificial Intelligence (cs.AI)

arXiv:2608.13774 [cs.AI]

(or arXiv:2608.13774v1 [cs.AI] for this version)

https://doi.org/10.48550/arXiv.2608.13774 arXiv-issued DOI via DataCite (pending registration)

https://doi.org/10.1137/25M1795194 DOI(s) linking to related resources