论文标题
基于惩罚回归花纹的广义添加剂模型中快速贝叶斯推断的拉普拉斯近似
Laplace approximation for fast Bayesian inference in generalized additive models based on penalized regression splines
论文作者
论文摘要
通用添加剂模型（GAM）是建立协变量之间复杂非线性关系和假定在指数族中有条件分布的响应之间的复杂非线性关系的统计工具。在本文中，P-Splines和Laplace近似是在游戏中的灵活且快速近似的贝叶斯推断中耦合的。拟议的Laplace-P-Spline模型有助于开发一种新方法，以考虑确定性网格策略或Markov链采样器，从而探索后惩罚空间，具体取决于预测指标中平滑添加术语的数量。我们的方法具有依靠近似后惩罚向量的梯度和黑森的封闭形式的分析表达式，这使得在相对较低的计算预算中，即使为大量的平滑添加成分，在相对较低的计算预算下，能够为潜在的现场变量构建准确的后验和可靠的集合估计器。基于条件潜在场后部的简单高斯近似值，建议的方法具有出色的统计特性。 Laplace-P-Spline模型的性能通过不同的模拟方案确认，并且在两个真实数据集上说明了该方法。
Generalized additive models (GAMs) are a well-established statistical tool for modeling complex nonlinear relationships between covariates and a response assumed to have a conditional distribution in the exponential family. In this article, P-splines and the Laplace approximation are coupled for flexible and fast approximate Bayesian inference in GAMs. The proposed Laplace-P-spline model contributes to the development of a new methodology to explore the posterior penalty space by considering a deterministic grid-based strategy or a Markov chain sampler, depending on the number of smooth additive terms in the predictor. Our approach has the merit of relying on closed form analytical expressions for the gradient and Hessian of the approximate posterior penalty vector, which enables to construct accurate posterior pointwise and credible set estimators for latent field variables at a relatively low computational budget even for a large number of smooth additive components. Based upon simple Gaussian approximations of the conditional latent field posterior, the suggested methodology enjoys excellent statistical properties. The performance of the Laplace-P-spline model is confirmed through different simulation scenarios and the method is illustrated on two real datasets.
