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

Embargo End Date
2022-11-12

Type
Article

Authors
Brown, Paul T.
Joshi, Chaitanya
Joe, Stephen
Rue, Haavard

KAUST Department
Statistics Program
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Preprint Posting Date
2019-11-22

Online Publication Date
2020-11-21

Print Publication Date
2021-05

Date
2020-11-21

Submitted Date
2019-11-22

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.

Citation
Brown, P. T., Joshi, C., Joe, S., & Rue, H. (2021). A novel method of marginalisation using low discrepancy sequences for integrated nested Laplace approximations. Computational Statistics & Data Analysis, 157, 107147. doi:10.1016/j.csda.2020.107147

Publisher
Elsevier BV

Journal
Computational Statistics & Data Analysis

DOI
10.1016/j.csda.2020.107147

arXiv
1911.09880

Additional Links
https://arxiv.org/pdf/1911.09880

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