A novel method of marginalisation using low discrepancy sequences for integrated nested Laplace approximations

Recently, it has been shown that the shape of a marginal distribution can be more accurately and efficiently captured using set low discrepancy sequence (LDS) points compared to standard grid points. This suggests use LDS could improve approximation posterior distributions produced by grid-based Bayesian methods such as Integrated Nested Laplace Approximation (INLA). However, obtaining posteriors is not straightforward. Two algorithms are proposed incorporated into INLA implementation approximate without sacrificing computational efficiency. examples also presented demonstrate algorithms, when used inside INLA, estimate than employs. A distinct advantage these capture multimodal shapes current numerical integration free algorithm (NIFA) method cannot.