Efficient quadratures for high-dimensional Bayesian data assimilation

Bayesian update is a common strategy used to combine (uncertain) model predictions and (noisy) observational data. A computational bottleneck in this data assimilation technique is the evaluation of high-dimensional quadratures involving multivariate probability density functions (PDFs) of system states. We explore “designed quadratures” as a means to reduce the computational cost of Bayesian update of multivariate joint PDFs. A series of numerical experiments demonstrate that our method outperforms stochastic collocation on sparse grids, a popular technique used to perform high-dimensional integration in the context of uncertainty quantification, in terms of both accuracy and computational efficiency.