文章基本信息

标题：Big Data Bayesian Linear Regression and Variable Selection by Normal-Inverse-Gamma Summation
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作者：Hang Qian
期刊名称：Bayesian Analysis
印刷版ISSN：1931-6690
电子版ISSN：1936-0975
出版年度：2018
卷号：13
期号：4
页码：1011-1035
DOI：10.1214/17-BA1083
语种：English
出版社：International Society for Bayesian Analysis
摘要：We introduce the normal-inverse-gamma summation operator, which combines Bayesian regression results from different data sources and leads to a simple split-and-merge algorithm for big data regressions. The summation operator is also useful for computing the marginal likelihood and facilitates Bayesian model selection methods, including Bayesian LASSO, stochastic search variable selection, Markov chain Monte Carlo model composition, etc. Observations are scanned in one pass and then the sampler iteratively combines normal-inversegamma distributions without reloading the data. Simulation studies demonstrate that our algorithms can efficiently handle highly correlated big data. A real-world data set on employment and wage is also analyzed.
关键词：conjugate prior; hierarchical shrinkage; MapReduce.