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.

中文翻译：

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一种使用低差异序列进行集成嵌套拉普拉斯近似的边缘化新方法

最近，已经表明，使用低差异序列 (LDS) 获得的边缘后验分布的近似值在准确性和计算效率方面都优于标准的基于网格的方法。这种最近的方法，我们将其称为 LDS-StM，也可以产生对多模态后验的良好近似。然而，将 LDS-StM 实施到集成嵌套拉普拉斯近似 (INLA) 中，这是一种使用基于网格的方法的方法，具有挑战性。受此问题的启发，我们建议对 LDS-StM 进行修改，以改进近似值并使其与 INLA 兼容，而不会牺牲计算速度。我们还提供了两个例子来证明经过修改的 LDS-StM 在速度和准确性方面可以优于 INLA 自己的网格近似。