We are seeking to characterize the performance and potential bottlenecks of the latest fast MCMC samplers. I see that Stan is currently using Intel TBB to parallelize the no-U-turn sampler (NUTS) across multiple chains. Do you know of any research attempted to parallelize each sampler itself within one chain. Our group at Google has been very interested in using parallel compute in HMC variants (including NUTS), particularly on accelerators (e.g., GPUs). We've been working in the deep-learning-oriented autodiff accelerator software frameworks TensorFlow and JAX, both of which are supported by our TensorFlow Probability library.