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Hamiltonian Monte Carlo has emerged as a standard tool for posteriorcomputation. In this article, we present an extension that can efficientlyexplore target distributions with discontinuous densities. Our extension inparticular enables efficient sampling from ordinal parameters though embeddingof probability mass functions into continuous spaces. We motivate our approachthrough a theory of discontinuous Hamiltonian dynamics and develop acorresponding numerical solver. The proposed solver is the first of its kind,with a remarkable ability to exactly preserve the Hamiltonian. We apply ouralgorithm to challenging posterior inference problems to demonstrate its wideapplicability and competitive performance.

Discontinuous Hamiltonian Monte Carlo for discrete parameters and discontinuous likelihoods