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首页> 外文期刊>Journal of the royal statistical society >Multivariate posterior inference for spatial models with the integrated nested Laplace approximation
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Multivariate posterior inference for spatial models with the integrated nested Laplace approximation

机译：具有集成嵌套拉普拉斯近似的空间模型的多元后验推论

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摘要

The integrated nested Laplace approximation (INLA) is a convenient way to obtain approximations to the posterior marginals for parameters in Bayesian hierarchical models when the latent effects can be expressed as a Gaussian Markov random field. In addition, its implementation in the R-INLA package for the R statistical software provides an easy way to fit models using the INLA in practice in a fraction of the time that other computer-intensive methods (e.g. Markov chain Monte Carlo methods) take to fit the same model. Although the INLA provides a fast approximation to the marginals of the model parameters, it is difficult to use it with models that are not implemented in R-INLA. It is also difficult to make multivariate posterior inference on the parameters of the model as the INLA focuses on the posterior marginals and not the joint posterior distribution. We describe how to use the INLA within the Metropolis-Hastings algorithm to fit complex spatial models and to estimate the joint posterior distribution of a small number of parameters. We illustrate the benefits of this new method with two examples. In the first, a spatial econometrics model with two auto-correlation parameters (for the response and the error term) is considered. This model is not currently available in R-INLA, and multivariate inference is often required to assess dependence between the two spatial auto-correlation parameters in the model. Furthermore, the estimation of spillover effects is based on the joint posterior distribution of a spatial auto-correlation parameter and a covariate coefficient. In the second example, a multivariate spatial model for several diseases is proposed for disease mapping. This model includes a shared specific spatial effect as well as disease-specific spatial effects. Dependence on the shared spatial effect is modulated via disease-specific weights. By inspecting the joint posterior distribution of these weights it is possible to assess which diseases have a similar spatial pattern.
机译：当潜在效应可以表示为高斯马尔可夫随机场时，集成嵌套拉普拉斯逼近（INLA）是获得贝叶斯层次模型中参数后边缘逼近的便捷方法。此外，它在R统计软件的R-INLA软件包中的实现为在实践中使用INLA拟合模型提供了一种简便的方法，而所需的时间却是其他计算机密集型方法（例如Markov链蒙特卡洛方法）花费的一小部分适合相同的模型。尽管INLA提供了模型参数边缘的快速近似值，但是很难将其与R-INLA中未实现的模型一起使用。由于INLA侧重于后边缘而不是关节后分布，因此很难对模型的参数进行多元后验。我们描述了如何在Metropolis-Hastings算法中使用INLA来拟合复杂的空间模型，并估计少量参数的联合后验分布。我们通过两个示例来说明这种新方法的好处。首先，考虑具有两个自相关参数（用于响应和误差项）的空间计量经济学模型。该模型当前在R-INLA中不可用，并且经常需要多变量推断来评估模型中两个空间自相关参数之间的依赖性。此外，溢出效应的估计是基于空间自相关参数和协变量系数的联合后验分布。在第二个示例中，提出了几种疾病的多元空间模型用于疾病映射。该模型包括共享的特定空间效应以及疾病特定的空间效应。对共享空间效应的依赖性通过疾病特异性权重来调节。通过检查这些权重的关节后部分布，可以评估哪些疾病具有相似的空间格局。

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