Adaptive schemes for piecewise deterministic Monte Carlo algorithms

The Bouncy Particle sampler (BPS) and the Zig-Zag (ZZS) are continuous time, non-reversible Monte Carlo methods based on piecewise deterministic Markov processes. Experiments show that speed of convergence these samplers can be affected by shape target distribution, as for instance in case anisotropic targets. We propose an adaptive scheme iteratively learns all or part covariance matrix takes advantage obtained information to modify underlying process with aim increasing convergence. Moreover, we define automatically tunes refreshment rate BPS ZZS. prove ergodicity a law large numbers proposed algorithms. Finally, benefits several numerical simulations.