Abstract
In this talk, I will discuss a birth-death dynamics for sampling multimodal probability distributions. At the continuum level, this dynamics is described by an infinite dimensional nonlinear and nonlocal ODE, which takes the target distribution as the unique invariant measure. The advantage of the birth-death dynamics is that it allows global move of the mass of a probability density directly from one mode to another in the phase space according to their relative weights, without the difficulty of going through low probability regions, suffered by any local dynamics such as the overdamped Langevin MCMC.
We prove that the birth death dynamics converges to the unique invariant measure with a uniform rate provided that the initial distribution, compared to the target, has strictly lower bound. We also propose a practical interacting particle sampling scheme as a numerical implementation of the kernelized version of birth death dynamics. The acceleration effect of birth-death for overdamped Langevin dynamics will be demonstrated via some analytical and numerical examples.