Enabling Bayesian uncertainty quantification for multiscale systems and network models via mutual likelihood-informed dimension reduction (A06+)

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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 the setting of many state or parameter inference problems associated to multiscale systems of interest to SFB 1114, such as precipitation and hurricane dynamics. 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 and transfer operator stacking, 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.