A partially collapsed Gibbs sampler for parameters with local constraints

We consider Bayesian detection/classification of discrete random parameters that are strongly dependent locally due to some deterministic local constraint. Based on the recently introduced partially collapsed Gibbs sampler (PCGS) principle, we develop a Markov chain Monte Carlo method that tolerates and even exploits the challenging probabilistic structure imposed by deterministic local constraints. We study the application of our method to the practically relevant case of nonuniformly spaced binary pulses with a known minimum distance. Simulation results demonstrate significant performance gains of our method compared to a recently proposed PCGS that is not specifically designed for the local constraint.