Toni Karvonen

My research focuses on uncertainty quantification and model misspecification in numerical analysis, statistical modelling, and machine learning. I want to understand how using a wrong model affects the reliability of uncertainty quantification in order to develop robust and data-efficient numerical and statistical methods. I am particularly interested in models and methods that make use of positive-definite kernels, such as Gaussian process regression and radial basis function interpolation. Topics that I have worked on include uncertainty quantification and hyperparameter estimation in Gaussian process modelling, error analysis for kernel-based approximation, information-based complexity, theory of reproducing kernel Hilbert spaces, probabilistic numerical methods, and non-linear state estimation.