Bayesian Scale Space Smoothing with Applications

The idea of a scale space has its origin in computer vision where it refers to a family of smooths of a digital image. No particular level of smoothing is regarded as "correct" and each smooth is thought to provide information about the object of the image at a particular scale, little smoothing revealing small details and heavy smoothing displaying only the coarsest features. Scale space analysis was only relatively recently introduced to Statistics by P. Chaudhuri and J.S. Marron in the form of SiZer methodology where the goal is to make inferences about scale-dependent features of curves and images from noisy observations. The talk describes a Bayesian version of SiZer. The advantages of the Bayesian approach includes straightforward simulation-based inference, flexibility in modeling the sources of uncertainty and the possibility to incorporate relevant prior information in the analyses. We discuss scale space analyses of paleoclimate reconstructions and suggest possible applications also to climate modeling and satellite based remote sensing.