华东师范大学学报(自然科学版) ›› 2004, Vol. 2004 ›› Issue (4): 33-39,9.

• 数学 统计学 • 上一篇    下一篇

非参数Bayes样条回归

卢一强1,2, 茆诗松2   

  1. 1.信息工程大学电子技术学院，郑州450004; 2.华东师范大学统计系，上海200062
  • 收稿日期:2002-09-30 修回日期:2003-04-25 出版日期:2004-12-25 发布日期:2004-12-25
  • 通讯作者: 卢一强

Bayesian Spline Nonparametric Regression

LU Yi-qiang1,2，MAO Shi-song2   

  1. 1. Institute of Electronic Technology，Information Engineering University，Zhengzhou 450004,China ; 2. Department of Statistics，East China Normal University，Shanghai 200062，China
  • Received:2002-09-30 Revised:2003-04-25 Online:2004-12-25 Published:2004-12-25
  • Contact: LU Yi-qiang

摘要：

对于非参数回归模型y= f(x)+ε，其中f (x)为光滑的连续函数.用样条函数来逼近f (x)，不具体选择结点的个数，考虑到结点个数的不确定性，给定结点个数一个均匀的无信息先验，用Bayes模型平均的方法来估计f (x).得到了f (x)的Bayes估计和Bayes后验区间估计.

关键词: Bayes模型平均, 可逆的跳MCMC抽样, 样条回归, Bayes因子, Bayes模型平均, 可逆的跳MCMC抽样, 样条回归, Bayes因子

Abstract: In this paper the nonparametric regression model y= f(x)+ε, where f (x) is a smoothing function, is considered. The nonparametric regression f (x) is approximated by a spline function. The knot number is not fixed but given a noninformation prior, by which the uncertainty of the knot number is studied. The regression f(x) is estimated by the method of Bayesian model averaging and the posterior interval is also estimated.

Key words: reversible jumped MCMC sampling, spline regression, Bayes factor, Bayesian model averaging, reversible jumped MCMC sampling, spline regression, Bayes factor

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