4 papers
Upper and lower bounds for local Lipschitz stability of Bayesian posteriors
Nada Cvetković, Han Cheng Lie
The work of Sprungk (Inverse Problems, 2020) established the local Lipschitz continuity of the misfit-to-posterior and prior-to-posterior maps with respect to the Kullback--Leibler…
Optimal low-rank approximations for linear Gaussian inverse problems on Hilbert spaces, Part I: posterior covariance approximation
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. Using t…
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…
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…