  Recently, a class of stochastic processes known as piecewise deterministic
Markov processes has been used to define continuous-time Markov chain Monte
Carlo algorithms with a number of attractive properties, including
compatibility with stochastic gradients like those typically found in
optimization and variational inference, and high efficiency on certain big data
problems. Not many processes in this class that are capable of targeting
arbitrary invariant distributions are currently known, and within one subclass
all previously known processes utilize linear transition functions. In this
work, we derive a process whose transition function is nonlinear through
solving its Fokker-Planck equation in hyperspherical coordinates. We explore
its behavior on Gaussian targets, as well as a Bayesian logistic regression
model with synthetic data. We discuss implications to both the theory of
piecewise deterministic Markov processes, and to Bayesian statisticians as well
as physicists seeking to use them for simulation-based computation.
