Variational Bayesian Inference for Parametric and Nonparametric Regression With Missing Data
Variational Bayesian Inference for Parametric and Nonparametric Regression With Missing Data
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DOI：
10.1198/jasa.2011.tm10301
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发表时间：
2011-09-01
影响因子：
3.7
通讯作者：
Wand, M. P.
中科院分区：
文献类型：
--
作者：
Faes, C.;Ormerod, J. T.;Wand, M. P.
当数据存在缺失时，贝叶斯分层模型是进行回归分析的有吸引力的结构。然而，必要的概率计算具有挑战性，通常采用蒙特卡罗方法。我们开发了一种基于确定性变分贝叶斯近似的替代方法。参数回归和非参数回归都被考虑。注意力仅限于更具挑战性的预测数据缺失情况。我们证明变分贝叶斯可以实现良好的准确性，但计算开销却要少得多。主要影响是在缺失数据的参数和非参数回归模型中快速近似贝叶斯推理。本文的在线版本附带补充材料。
Bayesian hierarchical models are attractive structures for conducting regression analyses when the data are subject to missingness. However, the requisite probability calculus is challenging and Monte Carlo methods typically are employed. We develop an alternative approach based on deterministic variational Bayes approximations. Both parametric and nonparametric regression are considered. Attention is restricted to the more challenging case of missing predictor data. We demonstrate that variational Bayes can achieve good accuracy, but with considerably less computational overhead. The main ramification is fast approximate Bayesian inference in parametric and nonparametric regression models with missing data. Supplemental materials accompany the online version of this article.