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Recently, a class of stochastic processes known as piecewise deterministicMarkov processes has been used to define continuous-time Markov chain MonteCarlo algorithms with a number of attractive properties, includingcompatibility with stochastic gradients like those typically found inoptimization and variational inference, and high efficiency on certain big dataproblems. Not many processes in this class that are capable of targetingarbitrary invariant distributions are currently known, and within one subclassall previously known processes utilize linear transition functions. In thiswork, we derive a process whose transition function is nonlinear throughsolving its Fokker-Planck equation in hyperspherical coordinates. We exploreits behavior on Gaussian targets, as well as a Bayesian logistic regressionmodel with synthetic data. We discuss implications to both the theory ofpiecewise deterministic Markov processes, and to Bayesian statisticians as wellas physicists seeking to use them for simulation-based computation.

A Piecewise Deterministic Markov Process via $(r,\theta)$ swaps in hyperspherical coordinates