  Sampling the parameters of high-dimensional Continuous Time Markov Chains
(CTMC) is a challenging problem with important applications in many fields of
applied statistics. In this work a recently proposed type of non-reversible
rejection-free Markov Chain Monte Carlo (MCMC) sampler, the Bouncy Particle
Sampler (BPS), is brought to bear to this problem. BPS has demonstrated its
favorable computational efficiency compared with state-of-the-art MCMC
algorithms, however to date applications to real-data scenario were scarce. An
important aspect of the practical implementation of BPS is the simulation of
event times. Default implementations use conservative thinning bounds. Such
bounds can slow down the algorithm and limit the computational performance. Our
paper develops an algorithm with an exact analytical solution to the random
event times in the context of CTMCs. Our local version of BPS algorithm takes
advantage of the sparse structure in the target factor graph and we also
provide a framework for assessing the computational complexity of local BPS
algorithms.
