Before revision:  We develop a new inference approach that exploits 1) the bouncy particle sampler  based on piecewise deterministic Markov processes  and 2) novel dynamic programming that reduces the cost of likelihood and gradient evaluations  to linear in sample size.
After revision:  We develop a new inference approach that exploits 1) the bouncy particle sampler (BPS) based on piecewise deterministic Markov processes and 2) novel dynamic programming that reduces the cost of likelihood and gradient evaluations to linear in sample size.