BAMLSS: Bayesian Additive Models for Location, Scale, and Shape (and Beyond)
BAMLSS: Bayesian Additive Models for Location, Scale, and Shape (and Beyond)
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DOI：
10.1080/10618600.2017.1407325
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发表时间：
2018-01-01
影响因子：
2.4
通讯作者：
Zeileis, Achim
中科院分区：
文献类型：
--
作者：
Umlauf, Nikolaus;Klein, Nadja;Zeileis, Achim
贝叶斯分析为复杂的广义加性回归模型 (GAM) 的估计提供了方便的设置。由于过去十年计算能力大幅提高，现在几乎可以在任何现代计算机上解决复杂的推理问题，例如使用马尔可夫链蒙特卡罗模拟。这是贝叶斯方法变得越来越流行的原因之一，导致出现了许多高度专业化和优化的估计引擎，并且注意力从条件均值模型转移到捕获响应分布的位置、规模、形状（和其他方面）的概率分布模型。为了嵌入文献和软件中建议的许多不同方法，建立了分布式 GAM 的统一建模架构，该架构利用分布、估计技术（后验模式或后验均值）和模型项（固定、随机、平滑、空间……）。结果表明，在这个框架内，实现复杂回归问题的算法以及现有软件的集成相对简单。两个复杂且计算要求高的应用案例研究强调了其有用性：大型日降水气候学，以及具有时空相互作用的连续时间的 Cox 模型。本文的补充材料可在线获取。
Bayesian analysis provides a convenient setting for the estimation of complex generalized additive regression models (GAMs). Since computational power has tremendously increased in the past decade, it is now possible to tackle complicated inferential problems, for example, with Markov chain Monte Carlo simulation, on virtually any modern computer. This is one of the reasons why Bayesian methods have become increasingly popular, leading to a number of highly specialized and optimized estimation engines and with attention shifting from conditional mean models to probabilistic distributional models capturing location, scale, shape (and other aspects) of the response distribution. To embed many different approaches suggested in literature and software, a unified modeling architecture for distributional GAMs is established that exploits distributions, estimation techniques (posterior mode or posterior mean), and model terms (fixed, random, smooth, spatial, ... ). It is shown that within this framework implementing algorithms for complex regression problems, as well as the integration of already existing software, is relatively straightforward. The usefulness is emphasized with two complex and computationally demanding application case studies: a large daily precipitation climatology, as well as a Cox model for continuous time with space-time interactions. Supplementary material for this article is available online.