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math.ST2025
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…
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.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…