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Sampling the parameters of high-dimensional Continuous Time Markov Chains(CTMC) is a challenging problem with important applications in many fields ofapplied statistics. In this work a recently proposed type of non-reversiblerejection-free Markov Chain Monte Carlo (MCMC) sampler, the Bouncy ParticleSampler (BPS), is brought to bear to this problem. BPS has demonstrated itsfavorable computational efficiency compared with state-of-the-art MCMCalgorithms, however to date applications to real-data scenario were scarce. Animportant aspect of the practical implementation of BPS is the simulation ofevent times. Default implementations use conservative thinning bounds. Suchbounds can slow down the algorithm and limit the computational performance. Ourpaper develops an algorithm with an exact analytical solution to the randomevent times in the context of CTMCs. Our local version of BPS algorithm takesadvantage of the sparse structure in the target factor graph and we alsoprovide a framework for assessing the computational complexity of local BPSalgorithms.

Analysis of high-dimensional Continuous Time Markov Chains using the Local Bouncy Particle Sampler