A Novel Method of Marginalisation using Low Discrepancy Sequences for Integrated Nested Laplace Approximations

TL;DR

This paper introduces a modified low discrepancy sequence method compatible with INLA, enhancing the accuracy and speed of marginal posterior approximations, especially for multimodal distributions.

Contribution

It proposes modifications to LDS-StM that improve approximation quality and integrate seamlessly with INLA, outperforming traditional grid-based methods.

Findings

LDS-StM with modifications outperforms INLA's grid approximation in speed.

The new method provides better accuracy for multimodal posteriors.

Demonstrated flexibility in approximating complex marginal distributions.

Abstract

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.