Robustness, model checking, and hierarchical models
针对层次模型（如潜在高斯模型）中假设难以检验的问题，提出通过定义放宽假设的替代模型来构建诊断统计量，并结合模型检验与稳健性分析的工作流程，以评估假设对结果的影响。
Abstract Model checking is essential to evaluate the adequacy of statistical models and the validity of inferences drawn from them. Particularly, hierarchical models such as latent Gaussian models (LGMs) pose unique challenges as it is difficult to check assumptions on the latent parameters. Diagnostic statistics are often used to quantify the degree to which a model fit deviates from the observed data. We construct diagnostic statistics by (a) defining an alternative model with relaxed assumptions and (b) deriving the diagnostic statistic most sensitive to discrepancies induced by this alternative model. We also promote a workflow for model criticism that combines model checking with subsequent robustness analysis. As a result, we obtain a general recipe to check assumptions in hierarchical models and the impact of these assumptions on the results. We demonstrate the ideas by assessing the latent Gaussianity assumption, a crucial but often overlooked assumption in LGMs. We illustrate the methods via examples utilizing Stan and provide functions for easy usage of the methods for general models fitted through R-INLA.