Latent jump fields for spatial statistics

Latent models are at the heart of modern statistical modeling. They are needed whenever the process of interest is observable only through indirect observations, such as measurements perturbed by noise. The joint model for the process and the observations is referred to as a latent model, and there exists a well-developed theory for these when the process is Gaussian. However, in areas ranging from longitudinal studies in biostatistics to geostatistics and climate science, there is a need for more general and still easy-to-use latent models. The goal of this project is to develop the theory and methods needed for latent jump fields, a class of such more general models constructed so that they can be used for research in spatial statistics involving big data.