Abstract

The integrated nested Laplace approximation (INLA) is a deterministic approach to Bayesian inference on latent Gaussian models (LGMs) and focuses on fast and accurate approximation of posterior marginals for the parameters in the models. Recently, methods have been developed to extend this class of models to those that can be expressed as conditional LGMs by fixing some of the parameters in the models to descriptive values. These methods differ in the manner descriptive values are chosen. This article proposes to combine importance sampling with INLA (IS-INLA), and extends this approach with the more robust adaptive multiple importance sampling algorithm combined with INLA (AMIS-INLA). This article gives a comparison between these approaches and existing methods on a series of applications with simulated and observed datasets and evaluates their performance based on accuracy, efficiency, and robustness. The approaches are validated by exact posteriors in a simple bivariate linear model; then, they are applied to a Bayesian lasso model, a Poisson mixture, a zero-inflated Poisson model and a spatial autoregressive combined model. The applications show that the AMIS-INLA approach, in general, outperforms the other methods compared, but the IS-INLA algorithm could be considered for faster inference when good proposals are available. Supplementary materials for this article are available online.

摘要

集成嵌套拉普拉斯近似 (INLA) 是对潜在高斯模型 (LGM) 进行贝叶斯推理的一种确定性方法，侧重于模型中参数的后边缘的快速准确近似。最近，通过将模型中的一些参数固定为描述性值，开发了一些方法将此类模型扩展到可以表示为条件 LGM 的模型。这些方法的不同之处在于选择描述性值的方式。本文提出将重要性采样与 INLA (IS-INLA) 相结合，并使用更鲁棒的自适应多重重要性采样算法与 INLA (AMIS-INLA) 相结合来扩展这种方法。本文对这些方法与现有方法在一系列具有模拟和观察数据集的应用程序上进行了比较，并根据准确性、效率和稳健性评估了它们的性能。这些方法通过简单的双变量线性模型中的精确后验验证；然后，将它们应用于贝叶斯套索模型、泊松混合模型、零膨胀泊松模型和空间自回归组合模型。应用程序表明，AMIS-INLA 方法总体上优于其他比较方法，但是当有好的建议可用时，可以考虑使用 IS-INLA 算法进行更快的推理。本文的补充材料可在线获取。然后，将它们应用于贝叶斯套索模型、泊松混合模型、零膨胀泊松模型和空间自回归组合模型。应用程序表明，AMIS-INLA 方法总体上优于其他比较方法，但是当有好的建议可用时，可以考虑使用 IS-INLA 算法进行更快的推理。本文的补充材料可在线获取。然后，将它们应用于贝叶斯套索模型、泊松混合模型、零膨胀泊松模型和空间自回归组合模型。应用程序表明，AMIS-INLA 方法总体上优于其他比较方法，但是当有好的建议可用时，可以考虑使用 IS-INLA 算法进行更快的推理。本文的补充材料可在线获取。