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math.ST2024
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…
math.FA2024
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…
math.ST2024
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…