A0269
Title: An unadjusted Barker algorithm for high-dimensional sampling without M-smoothness
Authors: Samuel Livingstone - University College London (United Kingdom) [presenting]
Abstract: The aim is to introduce a recently proposed skew-symmetric numerical scheme for stochastic differential equations. At each step, an innovation is generated by skewing a Gaussian random variable in the direction of the drift. If the level of skew is chosen appropriately it can be shown that the scheme accurately approximates the underlying diffusion process in both the weak and strong sense. Some results are shown about both the finite time and long time simulation, in the latter case applying the scheme to the overdamped Langevin diffusion. The scheme resembles an unadjusted version of the Barker proposal Metropolis-Hastings algorithm. A key feature is that no Lipschitz requirement on the drift is needed in order to establish strong convergence in the mean-squared sense or for a well-behaved sampling algorithm that converges geometrically quickly to an equilibrium with controllable discretization error.
