25 citations · 125 across the 21 of their papers we have counts for
21 papers
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…
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…
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…
Optimal low-rank posterior covariance approximation in linear Gaussian inverse problems on Hilbert spaces
Giuseppe Carere, Han Cheng Lie
For linear inverse problems with Gaussian priors and Gaussian observation noise, the posterior is Gaussian, with mean and covariance determined by the conditioning formula. The cov…
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…
Bayesian inference of covariate-parameter relationships for population modelling
Han Cheng Lie
We consider population modelling using parametrised ordinary differential equation initial value problems (ODE-IVPs). For each individual drawn randomly from the unknown population…
Choosing observation operators to mitigate model error in Bayesian inverse problems
Nada Cvetković, Han Cheng Lie, Harshit Bansal +1
In statistical inference, a discrepancy between the parameter-to-observable map that generates the data and the parameter-to-observable map that is used for inference can lead to m…
Dimension-independent Markov chain Monte Carlo on the sphere
H. C. Lie, D. Rudolf, B. Sprungk +1
We consider Bayesian analysis on high-dimensional spheres with angular central Gaussian priors. These priors model antipodally symmetric directional data, are easily defined in Hil…
Γ-convergence of Onsager-Machlup functionals. Part II: Infinite product measures on Banach spaces
Birzhan Ayanbayev, Ilja Klebanov, Han Cheng Lie +1
We derive Onsager-Machlup functionals for countable product measures on weighted subspaces of the sequence space . Each measure in the product is…
Γ-convergence of Onsager-Machlup functionals. Part I: With applications to maximum a posteriori estimation in Bayesian inverse problems
Birzhan Ayanbayev, Ilja Klebanov, Han Cheng Lie +1
The Bayesian solution to a statistical inverse problem can be summarised by a mode of the posterior distribution, i.e. a MAP estimator. The MAP estimator essentially coincides with…
Randomised one-step time integration methods for deterministic operator differential equations
Han Cheng Lie, Martin Stahn, T. J. Sullivan
Uncertainty quantification plays an important role in problems that involve inferring a parameter of an initial value problem from observations of the solution. Conrad et al.\ (\te…
Error bounds for some approximate posterior measures in Bayesian inference
Han Cheng Lie, T. J. Sullivan, Aretha Teckentrup
In certain applications involving the solution of a Bayesian inverse problem, it may not be possible or desirable to evaluate the full posterior, e.g. due to the high computational…
On a degeneracy ratio for bounded convex polytopes
Nada Cvetković, Han Cheng Lie
We consider a quantity that measures the roundness of a bounded, convex -polytope in . We majorise this quantity in terms of the smallest singular value of the mat…
Implicit Probabilistic Integrators for ODEs
Onur Teymur, Han Cheng Lie, Tim Sullivan +1
We introduce a family of implicit probabilistic integrators for initial value problems (IVPs), taking as a starting point the multistep Adams-Moulton method. The implicit construct…
Random forward models and log-likelihoods in Bayesian inverse problems
H. C. Lie, T. J. Sullivan, A. L. Teckentrup
We consider the use of randomised forward models and log-likelihoods within the Bayesian approach to inverse problems. Such random approximations to the exact forward model or log-…
Equivalence of weak and strong modes of measures on topological vector spaces
Han Cheng Lie, T. J. Sullivan
A strong mode of a probability measure on a normed space can be defined as a point such that the mass of the ball centred at uniformly dominates the mass of all other b…
Strong convergence rates of probabilistic integrators for ordinary differential equations
H. C. Lie, A. M. Stuart, T. J. Sullivan
Probabilistic integration of a continuous dynamical system is a way of systematically introducing model error, at scales no larger than errors introduced by standard numerical disc…
Quasi-invariance of countable products of Cauchy measures under non-unitary dilations
Han Cheng Lie, T. J. Sullivan
Consider an infinite sequence of independent Cauchy random variables, defined by a sequence of location parameters and a sequence…
Cameron-Martin theorems for sequences of symmetric Cauchy-distributed random variables
Han Cheng Lie, T. J. Sullivan
Given a sequence of Cauchy-distributed random variables defined by a sequence of location parameters and a sequence of scale parameters, we consider another sequence of random vari…
Convexity of a stochastic control functional related to importance sampling of Itô diffusions
Han Cheng Lie
We consider the problem of rare event importance sampling, where the random variable of interest is a path functional of an Itô diffusion computed up to the first exit from a -d…