Title: inlabru: software for fitting latent Gaussian models with non-linear predictors Show Chinese title

Title: inlabru：用于拟合带有非线性预测器的潜高斯模型的软件

Abstract: The integrated nested Laplace approximation (INLA) method has become a popular approach for computationally efficient approximate Bayesian computation. In particular, by leveraging sparsity in random effect precision matrices, INLA is commonly used in spatial and spatio-temporal applications. However, the speed of INLA comes at the cost of restricting the user to the family of latent Gaussian models and the likelihoods currently implemented in {INLA}, the main software implementation of the INLA methodology. {inlabru} is a software package that extends the types of models that can be fitted using INLA by allowing the latent predictor to be non-linear in its parameters, moving beyond the additive linear predictor framework to allow more complex functional relationships. For inference it uses an approximate iterative method based on the first-order Taylor expansion of the non-linear predictor, fitting the model using INLA for each linearised model configuration. {inlabru} automates much of the workflow required to fit models using {R-INLA}, simplifying the process for users to specify, fit and predict from models. There is additional support for fitting joint likelihood models by building each likelihood individually. {inlabru} also supports the direct use of spatial data structures, such as those implemented in the {sf} and {terra} packages. In this paper we outline the statistical theory, model structure and basic syntax required for users to understand and develop their own models using {inlabru}. We evaluate the approximate inference method using a Bayesian method checking approach. We provide three examples modelling simulated spatial data that demonstrate the benefits of the additional flexibility provided by {inlabru}. Show Chinese abstract

Abstract: 集成嵌套拉普拉斯近似（INLA）方法已成为一种计算高效的近似贝叶斯计算的流行方法。 特别是，通过利用随机效应精度矩阵中的稀疏性，INLA 常用于空间和时空应用中。 然而，INLA 的速度是以限制用户只能使用潜高斯模型族以及目前实现于 {INLA}（INLA 方法的主要软件实现）中的似然函数为代价的。 {实验室}是一个软件包，通过允许潜在预测器在其参数中是非线性的，从而扩展了可以使用 INLA 拟合的模型类型，突破了加性线性预测器框架，以允许更复杂的函数关系。 对于推断，它使用基于非线性预测器一阶泰勒展开的近似迭代方法，针对每个线性化的模型配置使用 INLA 拟合模型。 {实验室}自动化了许多使用 {R-INLA}拟合模型所需的流程，简化了用户指定、拟合和从模型中预测的过程。 还提供了对联合似然模型拟合的额外支持，通过分别构建每个似然函数来实现。 {实验室}还支持直接使用空间数据结构，例如在 {sf}和 {terra}包中实现的那些。 本文概述了用户理解和开发基于{实验室}的模型所需的统计理论、模型结构和基本语法。 我们采用贝叶斯方法检验的方式评估了近似推理方法。 我们提供了三个模拟空间数据的建模示例，这些示例展示了{实验室}提供的额外灵活性的优势。