Spatial Models with the Integrated Nested Laplace Approximation within Markov Chain Monte Carlo
Spatial Models with the Integrated Nested Laplace Approximation within Markov Chain Monte Carlo
复制标题
马尔可夫链蒙特卡罗内集成嵌套拉普拉斯近似的空间模型
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
Francisco Palm'i
中科院分区：
文献类型：
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作者：
Virgilio G'omez;Francisco Palm'i
当潜在效应可以表示为高斯马尔可夫随机场（GMRF）时，积分嵌套拉普拉斯近似（INLA）是获得贝叶斯层次模型参数后验边际近似值的一种方便方法。此外，它在R统计软件的R-INLA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。R-INLA实现了许多广泛使用的潜在模型，包括几个空间模型。此外，与其他计算机密集型方法（例如马尔可夫链蒙特卡罗）相比，R-INLA可以在一小部分时间内拟合模型来拟合相同的模型。
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 (GMRF). In addition, its implementation in the R-INLA package for the R statistical software provides an easy way to fit models using INLA in practice. R-INLA implements a number of widely used latent models, including several spatial models. In addition, R-INLA can fit models in a fraction of the time than other computer intensive methods (e.g. Markov Chain Monte Carlo) take to fit the same model.
Although INLA provides a fast approximation to the marginals of the model parameters, it is difficult to use it with models not implemented in R-INLA. It is also difficult to make multivariate posterior inference on the parameters of the model as INLA focuses on the posterior marginals and not the joint posterior distribution.
In this paper we describe how to use INLA within the Metropolis-Hastings algorithm to fit spatial models and estimate the joint posterior distribution of a reduced number of parameters. We will illustrate the benefits of this new method with two examples on spatial econometrics and disease mapping where complex spatial models with several spatial structures need to be fitted.