Bayesian isotonic density regression.
Bayesian isotonic density regression.
复制标题
贝叶斯等渗密度回归。
DOI：
10.1093/biomet/asr025
复制
发表时间：
2011
期刊：
影响因子：
2.7
通讯作者：
Dunson,DavidB
中科院分区：
文献类型：
--
作者：
Wang,Lianming;Dunson,DavidB
密度回归模型允许给定预测器的响应的条件分布在预测器空间上灵活地变化。这种模型比带有非参数残差分布的非参数均值回归模型灵活得多，在许多应用中得到了很好的支持。对于密度回归，已经提出了各种各样的贝叶斯方法，但尚不清楚这些先验是否有充分的支持，因此任何真正的数据生成模型都可以准确地近似。本文发展了一类新的密度回归模型，该模型包含随机排序约束，当响应倾向于随预测器单调增加或减少时，这种约束是自然的。理论的发展显示出很大的支持。方法开发的假设检验，后验计算依赖于一个简单的吉布斯采样器。在模拟研究中说明了频率特性，并考虑了流行病学的应用。
Density regression models allow the conditional distribution of the response given predictors to change flexibly over the predictor space. Such models are much more flexible than nonparametric mean regression models with nonparametric residual distributions, and are well supported in many applications. A rich variety of Bayesian methods have been proposed for density regression, but it is not clear whether such priors have full support so that any true data-generating model can be accurately approximated. This article develops a new class of density regression models that incorporate stochastic-ordering constraints which are natural when a response tends to increase or decrease monotonely with a predictor. Theory is developed showing large support. Methods are developed for hypothesis testing, with posterior computation relying on a simple Gibbs sampler. Frequentist properties are illustrated in a simulation study, and an epidemiology application is considered.