7 papers
Goal-oriented learning of stochastic differential equations using error bounds on path-space observables
Joanna Zou, Han Cheng Lie, Youssef Marzouk
Stochastic differential equations (SDEs), which serve as the governing equations for dynamical systems in a broad range of applications, can become cost-prohibitive for numerical s…
Posterior error bounds for prior-driven balancing in linear Gaussian inverse problems
Josie König, Han Cheng Lie
In large-scale Bayesian inverse problems, it is often necessary to apply approximate forward models to reduce the cost of forward model evaluations, while controlling approximation…
Error bounds for approximate posteriors from likelihood-informed reduced-order models
Han Cheng Lie, Jakob Scheffels, Elisabeth Ullmann
In the design of computational methods for Bayesian inverse problems, costly forward model evaluations make it difficult to sample from or compute the posterior. This motivates the…
Generalised Rank-Constrained Approximations of Hilbert-Schmidt Operators on Separable Hilbert Spaces and Applications
Giuseppe Carere, Han Cheng Lie
In this work we solve, for given bounded operators and Hilbert-Schmidt operator acting on potentially infinite-dimensional separable Hilbert spaces, the reduced rank appr…
Optimal low-rank posterior mean and distribution approximation in linear Gaussian inverse problems on Hilbert spaces
Giuseppe Carere, Han Cheng Lie
We construct optimal low-rank approximations for the Gaussian posterior distribution in linear Gaussian inverse problems with possibly infinite-dimensional separable Hilbert parame…
Goodness-of-fit testing for nonlinear inverse problems with random observations
Remo Kretschmann, Han Cheng Lie
This work is concerned with nonparametric goodness-of-fit testing in the context of nonlinear inverse problems with random observations. Bayesian posterior distributions based upon…