论文标题
扩展的简化拉普拉斯策略，用于使用R-Inla近似潜在高斯模型的贝叶斯推断
An Extended Simplified Laplace strategy for Approximate Bayesian inference of Latent Gaussian Models using R-INLA
论文作者
论文摘要
将贝叶斯推理方法应用于复杂的层次模型时，会出现各种计算挑战。基于抽样的推理方法，例如马尔可夫链蒙特卡洛策略，以提供准确的结果，但具有较高的计算成本，缓慢或可疑的融合而闻名。相反，诸如集成的嵌套拉普拉斯近似（INLA）之类的近似方法通过嵌套的拉普拉斯近似构建了对单变量后代的确定性近似。此方法可以在潜在高斯模型中快速推理性能，该模型编码了一大类层次模型。 R-INLA软件主要包括三种策略，以根据精度要求计算所有必需的后近似值。简化的拉普拉斯近似（SLA）是最吸引人的，因为它的速度性能是基于泰勒膨胀，直至完整的拉普拉斯近似的三个订单。在这里，我们通过简化偏度和模态配置所需的计算来增强方法。然后，我们提出一个扩展以订购四个，并将扩展偏斜的正态分布作为新的参数拟合。与SLA计算的近似值相比，对边缘后密度的近似值更准确，基本上没有额外的成本。
Various computational challenges arise when applying Bayesian inference approaches to complex hierarchical models. Sampling-based inference methods, such as Markov Chain Monte Carlo strategies, are renowned for providing accurate results but with high computational costs and slow or questionable convergence. On the contrary, approximate methods like the Integrated Nested Laplace Approximation (INLA) construct a deterministic approximation to the univariate posteriors through nested Laplace Approximations. This method enables fast inference performance in Latent Gaussian Models, which encode a large class of hierarchical models. R-INLA software mainly consists of three strategies to compute all the required posterior approximations depending on the accuracy requirements. The Simplified Laplace approximation (SLA) is the most attractive because of its speed performance since it is based on a Taylor expansion up to order three of a full Laplace Approximation. Here we enhance the methodology by simplifying the computations necessary for the skewness and modal configuration. Then we propose an expansion up to order four and use the Extended Skew Normal distribution as a new parametric fit. The resulting approximations to the marginal posterior densities are more accurate than those calculated with the SLA, with essentially no additional cost.
