  Priors with a NUV representation (normal with unknown variance) have mostly
been used for sparsity. In this paper, a novel NUV prior is proposed that
effectively binarizes. While such a prior may have many uses, in this paper, we
explore its use for discrete-level control (with M $\geq$ 2 levels) including,
in particular, a practical scheme for digital-to-analog conversion. The
resulting computations, for each planning period, amount to iterating
forward-backward Gaussian message passing recursions (similar to Kalman
smoothing), with a complexity (per iteration) that is linear in the planning
horizon. In consequence, the proposed method is not limited to a short planning
horizon and can therefore outperform "optimal" methods. A preference for sparse
level switches can easily be incorporated.
