We consider two sets of new priors for Bayesian inversion and machine learning: The first one is based on mixture of experts models with Gaussian processes. The target is to estimate the number of experts and their parameters, and to make state estimation. For sampling, we use SMC^2. For non-Gaussian priors, we discuss Cauchy priors and the generalisation to high-order Cauchy fields and further generalisation to alpha-stable fields. For sampling, we use a selection of modern MCMC tools. Finally, we apply some of the methods and models to an industrial tomography problem on estimating log internal structure, measured at sawmills, based on X-ray, RGB camera and laser scanning.
Lassi Roininen holds the position of Associate Professor (tenure track) in applied mathematics in LUT University, Finland. He is also a docent in applied mathematics at the University of Oulu, Finland. He develops rigorous numerical and computational tools for inverse problems with applications in near-space remote sensing, subsurface imaging, and X-ray tomography.