Moraga Paula, Dean Christopher, Inoue Joshua, Morawiecki Piotr, Noureen Shahzeb Raja, Wang Fengpei
Computer, Electrical and Mathematical Sciences and Engineering Division, King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Saudi Arabia.
Department of Mathematical Sciences, University of Bath, Bath, Somerset, BA2 7AY, UK.
Spat Spatiotemporal Epidemiol. 2021 Nov;39:100440. doi: 10.1016/j.sste.2021.100440. Epub 2021 Aug 3.
Bayesian spatial models are widely used to analyse data that arise in scientific disciplines such as health, ecology, and the environment. Traditionally, Markov chain Monte Carlo (MCMC) methods have been used to fit these type of models. However, these are highly computationally intensive methods that present a wide range of issues in terms of convergence and can become infeasible in big data problems. The integrated nested Laplace approximation (INLA) method is a computational less-intensive alternative to MCMC that allows us to perform approximate Bayesian inference in latent Gaussian models such as generalised linear mixed models and spatial and spatio-temporal models. This approach can be used in combination with the stochastic partial differential equation (SPDE) approach to analyse geostatistical data that have been collected at particular sites to predict the spatial process underlying the data as well as to assess the effect of covariates and model other sources of variability. Here we demonstrate how to fit a Bayesian spatial model using the INLA and SPDE approaches applied to freely available data of malaria prevalence and risk factors in Mozambique. We show how to fit and interpret the model to predict malaria risk and assess the effect of covariates using the R-INLA package, and provide the R code necessary to reproduce the results or to use it in other spatial applications.
贝叶斯空间模型被广泛用于分析健康、生态和环境等科学学科中产生的数据。传统上，马尔可夫链蒙特卡罗（MCMC）方法已被用于拟合这类模型。然而，这些都是计算量极大的方法，在收敛方面存在一系列问题，并且在大数据问题中可能变得不可行。集成嵌套拉普拉斯近似（INLA）方法是一种计算量较小的替代MCMC的方法，它使我们能够在潜在高斯模型（如广义线性混合模型以及空间和时空模型）中进行近似贝叶斯推断。这种方法可以与随机偏微分方程（SPDE）方法结合使用，以分析在特定地点收集的地质统计数据，预测数据背后的空间过程，以及评估协变量的影响并对其他变异性来源进行建模。在这里，我们展示了如何使用INLA和SPDE方法拟合贝叶斯空间模型，该模型应用于莫桑比克疟疾流行率和风险因素的免费可用数据。我们展示了如何使用R-INLA软件包拟合和解释该模型以预测疟疾风险并评估协变量的影响，并提供重现结果或在其他空间应用中使用它所需的R代码。
