标题： 具有马尔可夫链蒙特卡罗的集成嵌套拉普拉斯近似的空间模型 显示英文标题

标题： Spatial Models with the Integrated Nested Laplace Approximation within Markov Chain Monte Carlo

摘要： 集成嵌套拉普拉斯近似（INLA）是一种方便的方法，用于在潜在效应可以表示为高斯马尔可夫随机场（GMRF）时，获得贝叶斯分层模型中参数的后验边缘近似值。 此外，R-INLA包在R统计软件中的实现为实际使用INLA拟合模型提供了简便的方法。 R-INLA实现了多种广泛使用的潜在模型，包括几种空间模型。 此外，R-INLA可以在比其他计算密集型方法（例如马尔可夫链蒙特卡洛）拟合相同模型所需时间的几分之一时间内拟合模型。 尽管INLA提供了对模型参数边缘的快速近似，但很难将其用于R-INLA中未实现的模型。 同时，由于INLA专注于后验边缘而非联合后验分布，因此很难对模型参数进行多变量后验推断。 在本文中，我们描述了如何在Metropolis-Hastings算法中使用INLA来拟合空间模型并估计少量参数的联合后验分布。 我们将通过两个关于空间计量经济学和疾病映射的例子来说明这种方法的优势，这些例子需要拟合具有多个空间结构的复杂空间模型。 显示英文摘要

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 (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.