BIMC: The Bayesian Inverse Monte Carlo method for goal-oriented uncertainty quantification. Part I

Understand

We consider the problem of estimating rare event probabilities, focusing on systems whose evolution is governed by differential equations with uncertain input parameters.

• If the system dynamics is expensive to compute, standard sampling algorithms such as the Monte Carlo method may require infeasible running times to accurately evaluate these probabilities.
• We propose an importance sampling scheme (which we call BIMC) that relies on solving an auxiliary, fictitious Bayesian inverse problem.
• The solution of the inverse problem yields a posterior PDF, a local Gaussian approximation to which serves as the importance sampling density.