  Multilevel Stein variational gradient descent is a method for particle-based
variational inference that leverages hierarchies of surrogate target
distributions with varying costs and fidelity to computationally speed up
inference. The contribution of this work is twofold. First, an extension of a
previous cost complexity analysis is presented that applies even when the
exponential convergence rate of single-level Stein variational gradient descent
depends on iteration-varying parameters. Second, multilevel Stein variational
gradient descent is applied to a large-scale Bayesian inverse problem of
inferring discretized basal sliding coefficient fields of the Arolla glacier
ice. The numerical experiments demonstrate that the multilevel version achieves
orders of magnitude speedups compared to its single-level version.
