Ieva’s research centres around Bayesian inference with a focus on inverse problems and uncertainty quantification in physics-based problems. These areas provide frameworks for making informed decisions in the presence of uncertainty, which is inherent in complex systems like climate modelling and environmental prediction. Inverse problems, in particular, are fundamental in reconstructing unknown quantities from observed data, a common challenge in fields such as geophysics and engineering.

The primary methodologies utilised and developed in her work are Gaussian processes for modelling complex spatial and temporal dependencies, and variational inference for scalable posterior estimation in high-dimensional Bayesian models. Applying these techniques to partial differential equation (PDE) based inverse problems and experimental design is of particular interest. 

In recent years, Ieva has worked on interdisciplinary projects in climate modelling, focusing on experimental design for ice sheet modelling and analysis on climate simulator data, carried out in partnerships with the British Antarctic Survey. 

Prior to joining LSE, Ieva held a Senior Research Fellowship in Statistical Science at UCL and a Biometrika Postdoctoral Research Fellowship at the University of Cambridge.