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