Integrated nested Laplace approximation provides accurate and efficient approximations for marginal distributions in latent Gaussian random field models. Computational feasibility of the original Rue et al. (2009) methods relies on efficient approximation of Laplace approximations for the marginal distributions of the coefficients of the latent field, conditional on the data and hyperparameters. The computational efficiency of these approximations depends on the Gaussian field having a Markov structure. This note provides equivalent efficiency without requiring the Markov property, which allows for straightforward use of latent Gaussian fields without a sparse structure, such as reduced rank multi-dimensional smoothing splines. The method avoids the approximation for conditional modes used in Rue et al. (2009), and uses a log determinant approximation based on a simple quasi-Newton update. The latter has a desirable property not shared by the most commonly used variant of the original method.

中文翻译：

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简化的集成嵌套拉普拉斯近似

集成的嵌套拉普拉斯逼近可为潜在高斯随机场模型中的边际分布提供准确而有效的逼近。原始Rue等人的计算可行性。（2009年）的方法依赖于Laplace近似的有效近似，以数据和超参数为条件的潜场系数的边际分布。这些近似的计算效率取决于具有马尔可夫结构的高斯场。本说明无需Markov属性即可提供等效的效率，该属性允许在不使用稀疏结构（例如降低秩的多维平滑样条）的情况下直接使用潜在的高斯场。该方法避免了Rue等人中使用的条件模式的近似。（2009），并使用基于简单拟牛顿更新的对数行列式近似。后者具有原始方法最常用的变体所不具有的理想属性。