  Irreversible and rejection-free Monte Carlo methods, recently developed in
Physics under the name Event-Chain and known in Statistics as Piecewise
Deterministic Monte Carlo (PDMC), have proven to produce clear acceleration
over standard Monte Carlo methods, thanks to the reduction of their random-walk
behavior. However, while applying such schemes to standard statistical models,
one generally needs to introduce an additional randomization for sake of
correctness. We propose here a new class of Event-Chain Monte Carlo methods
that reduces this extra-randomization to a bare minimum. We compare the
efficiency of this new methodology to standard PDMC and Monte Carlo methods.
Accelerations up to several magnitudes and reduced dimensional scalings are
exhibited.
