4 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…
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…
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…