Regression models in which a response variable is related to smooth functions of some predictor variables are popular as a result of their appealing balance between flexibility and interpretability. Since the original generalized additive models of Hastie and Tibshirani (Generalized additive models. Chapman & Hall, Boca Raton, 1990) numerous model extensions have been proposed, and a variety of practically useful computational strategies have emerged. This paper provides an overview of some widely applicable frameworks for this type of modelling, emphasizing the similarities between the different approaches, and the equivalence of smoothing, Gaussian latent process models and Gaussian random effects. The focus is particularly on Bayes empirical smoother theory, fully Bayesian inference via stochastic simulation or integrated nested Laplace approximation and boosting.

中文翻译：

---

广义加性模型及其扩展的推理和计算

响应模型与某些预测变量的平滑函数相关的回归模型由于其在灵活性和可解释性之间具有吸引力的平衡而广受欢迎。自从Hastie和Tibshirani的原始广义可加模型（广义可加模型，Chapman＆Hall，博卡拉顿，1990年）以来，已经提出了许多模型扩展，并且出现了许多实际有用的计算策略。本文概述了用于这种类型建模的一些可广泛应用的框架，强调了不同方法之间的相似性以及平滑的等效性，高斯潜在过程模型和高斯随机效应。重点是贝叶斯经验平滑理论，