Bouncy particle sampler with infinite exchanging parallel tempering

Markov chain Monte Carlo is one of the most useful tools for obtaining samples from complex distributions, such as posterior distributions in Bayesian inference. Bouncy particle sampler (BPS) is a method that performs sampling using uniform linear motion and elastic collisions. Since BPS does not require time discretization, it is expected to be more advantageous than the widely used Hamiltonian Monte Carlo (HMC) and Langevin Monte Carlo (LMC) for distributions with large curvature changes. To sample more efficiently from multimodal distributions, we propose BPS with parallel tempering (BPS-PT) in the infinite exchange limit, based on LMC-PT with the infinite exchange rate proposed in a previous study. Using a distribution with large curvature changes, BPS-PT showed estimation accuracy comparable to HMC-PT and LMC-PT, and achieved higher ESS per computational time. Therefore, BPS-PT is considered to be effective for distributions with large curvature changes.