Monte Carlo methods are the computational workhorse of statistical inference as applied to inverse problems throughout the physical sciences, but can become prohibitively costly when inferring high-dimensional or coupled parameters. This is exactly the setting of many state or parameter inference problems associated to multiscale systems of interest to SFB 1114. We propose to use a combination of strategies drawn from established traditions such as multilevel and adaptive Monte Carlo, and novel contributions such as likelihood-informed active subspace dimension reduction, to reduce the effective computational dimension, thereby accelerating convergence and reducing computational cost, while also studying and controlling the impact of the approximation errors incurred.
Klus, S. and Schuster, I. and Muandet, K. (2017) Eigendecompositions of Transfer Operators in Reproducing Kernel Hilbert Spaces. SFB 1114 Preprint in SciRate arXiv:1712.01572 . pp. 1-33. (Unpublished)
Schuster, I. and Constantine, P.G. and Sullivan, T.J. (2017) Exact active subspace Metropolis-Hastings, with applications to the Lorenz-96 system. SFB 1114 Preprint in arXiv:1712.02749 . pp. 1-10. (Unpublished)