Despite the ever-increasing amounts observations available in the age of big data, observations are often limited to smaller spatial extents or timescales than the studied processes. In this context, the answers to many problems lie in models that cannot be uniquely constrained given available data. Such an inference process leaves unanswered basic questions about any model: How unique is a given model? How much does each observation contribute to the model? What is the impact of errors in the model? How reliable are predictions made from the model?

To address these questions, this project focuses on applying full Bayesian analysis techniques to large ill-posed inverse problems in solid earth geophysics including but not limited to earthquake source inversions and seismic imaging techniques. This project also investigates other fields such as volcanology, glaciology and astrophysics. Bayesian analysis is a powerful tool to combine theoretical knowledge with measurements in order to address scientific problems probabilistically. This project is particularly challenging given the high-dimensionality and ill-posed nature of investigated inversion problems. Another significant challenge is to develop appropriate stochastic models that will reflect uncertainties in our theoretical predictions, which are currently neglected