Efficient Bayesian Sampling with Langevin Birth-Death Dynamics

Abstract: Bayesian inference plays a central role in scientific and engineering applications by enabling principled reasoning under uncertainty. However, sampling from generic probability distributions remains a computationally demanding task. This difficulty is compounded when the distributions are ill-conditioned, multi-modal, or supported on topologically non-Euclidean spaces. Motivated by challenges in gravitational wave parameter estimation, we propose simulating a Langevin diffusion augmented with a birth-death process. The dynamics are rescaled with a simple preconditioner, and generalized to apply to the product spaces of a hypercube and hypertorus. Our method is first-order and embarrassingly parallel with respect to model evaluations, making it well-suited for algorithmic differentiation and modern hardware accelerators. We validate the algorithm on a suite of toy problems and successfully apply it to recover the parameters of GW150914 -- the first observed binary black hole merger. This approach addresses key limitations of traditional sampling methods, and introduces a template that can be used to design robust samplers in the future.