On NUP Priors and Gaussian Message Passing
Hans‐Andrea Loeliger · 2023
Normals with unknown parameters (NUP) can represent many useful priors, and they allow to convert nontrivial model-based estimation problems into iterations of least-squares problems or linear-Gaussian estimation problems. Sparsity inducing NUP priors have been known for some time, and NUP priors for enforcing inequality constraints and discrete-level constraints have been proposed recently. We review this approach, and we develop it further by proposing a NUP representation of certain non-Gaussian messages that occur in hierarchical models. For illustration, we use a state space model with piecewise constant observation noise variance.