PhD thesis defence, 16 June - Lassi Roininen

Right on, it is finally time to have my public PhD thesis defence. The location and time are: Sodankylä Geophysical Observatory on 16 June at 12 o'clock.

The title of the thesis is "Discretisation-invariant and computationally efficient correlation priors for Bayesian inversion".

There will be two opponents: Professor Håvard Rue from NTNU/Trondheim. He is well-known e.g. on his book on Gaussian Markov random fields and R-INLA software. The second opponent is Professor Jouko Lampinen from Aalto University. He is director of the Dept of Computer Science at Aalto University.

Following the tradition, the thesis defence is open for public. Hence, welcome anyone interested!

... and finally, here's the abstract of the thesis.

Abstract: We are interested in studying  Gaussian Markov random fields as   correlation priors for Bayesian inversion. We construct the correlation priors to be discretisation-invariant, which means, loosely speaking, that the discrete  priors converge to continuous priors at the discretisation limit. We construct the priors with stochastic partial differential equations, which guarantees computational efficiency via sparse matrix approximations. The stationary correlation priors have a clear statistical interpretation through the autocorrelation function.

We also consider how to make structural model of an unknown object with anisotropic and inhomogeneous Gaussian Markov random fields. Finally we consider these fields on unstructured meshes, which are needed on complex domains.

The publications in this thesis contain fundamental mathematical and computational results of correlation priors. We have considered one application in this thesis, the electrical impedance tomography. These fundamental results and application provide a platform for engineers and researchers to use correlation priors in other inverse problem applications.