  Recently, it has been shown that approximations to marginal posterior
distributions obtained using a low discrepancy sequence (LDS) can outperform
standard grid-based methods with respect to both accuracy and computational
efficiency. This recent method, which we will refer to as LDS-StM, can also
produce good approximations to multimodal posteriors. However, implementation
of LDS-StM into integrated nested Laplace approximations (INLA), a methodology
in which grid-based methods are used, is challenging. Motivated by this
problem, we propose modifications to LDS-StM that improves the approximations
and make it compatible with INLA, without sacrificing computational speed. We
also present two examples to demonstrate that LDS-StM with modifications can
outperform INLA's own grid approximation with respect to speed and accuracy. We
also demonstrate the flexibility of the new approach for the approximation of
multimodal marginals.
