Research

Marginalization of Hyperparameters in Bayesian Inverse Problems

In joint work with my advisor Georg Stadler, I am working on developing methods of marginalizing out the effects of unknown hyperparameters on linear PDE-governed Bayesian inverse problems (BIPs). In particular, BIPs with Gaussian priors can be represented as Latent Gaussian Models, for which popular methods such as Integrated Nested Laplace Approximations have been developed. My work extends these ideas, typically used in spatial statistics, to PDE-governed problems, which have fundamentally different challenges due to the computational cost of repeated PDE solves. Our methods take advantage of low rank structures in these problems to accelerate sampling and integration of the marginal distributions.

For more information, see this poster from March 2026 or these slides from July 2025.