The accelerated results from the preceding lecture all operate in continuous time; how can we translate them to algorithmic implementations? I will discuss a class of samplers based on piecewise deterministic Markov processes. In particular, I will introduce a new algorithm called the proximal bouncy particle sampler (or proximal BPS), developed with co-authors Fan Chen, Jianfeng Lu, and Matthew S. Zhang. The algorithm combines the proximal sampler with persistence across iterations, and we will show that it admits an accelerated discrete-time hypocoercive analysis.