25 citations · 125 across the 21 of their papers we have counts for
9 papers · 1 filter
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…
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…
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…
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-…