We study estimation and variable selection in non-Gaussian Bayesian generalized additive models (GAMs) under a spike-and-slab prior for grouped variables. Our framework subsumes GAMs for logistic regression, Poisson regression, negative binomial regression, and gamma regression, and encompasses both canonical and non-canonical link functions. Under mild conditions, we establish posterior contraction rates and model selection consistency when $p \gg n$. For computation, we propose an EM algorithm for obtaining MAP estimates in our model, which is available in the R package sparseGAM. We illustrate our method on both synthetic and real data sets.

翻译：我们研究非高加索湾通用添加剂模型(GAMs)的估算和变量选择,在分类变量之前先用钉杆和板块进行分类。我们的框架包含物流回归、Poisson回归、负二进制回归和伽马回归的GAMs子集,同时包括卡通和非卡门联系功能。在温和的条件下,我们在$p\gg n美元时确定后继收缩率和模型选择一致性。在计算时,我们提出一个EM算法,以便在我们的模型中获取MAP估计数,该算法可在R包稀释GAM中找到。我们在合成数据集和真实数据集上都展示了我们的方法。