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In this work we present a non-reversible, tuning- and rejection-free Markovchain Monte Carlo which naturally fits in the framework of hit-and-run. Thesampler only requires access to the gradient of the log-density function, hencethe normalizing constant is not needed. We prove the proposed Markov chain isinvariant for the target distribution and illustrate its applicability througha wide range of examples. We show that the sampler introduced in the presentpaper is intimately related to the continuous sampler of Peters and de With(2012), Bouchard-Cote et al. (2017). In particular, the computation is quitesimilar in the sense that both are centered around simulating an inhomogenuousPoisson process. The computation can be simplified when the gradient of thelog-density admits a computationally efficient directional decomposition into asum of two monotone functions. We apply our sampler in selective inference,gaining significant improvement over the formerly used sampler (Tian et al.2016).

Non-reversible, tuning- and rejection-free Markov chain Monte Carlo via iterated random functions