Bayesian smoothing and regression splines for measurement error problems
Bayesian smoothing and regression splines for measurement error problems
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DOI：
10.1198/016214502753479301
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发表时间：
2002-03-01
影响因子：
3.7
通讯作者：
Ruppert, D
中科院分区：
文献类型：
--
作者：
Berry, SM;Carroll, RJ;Ruppert, D
在存在协变量测量误差的情况下，非参数地估计回归函数是极其困难的，该问题与去卷积有关。对于这个问题，存在各种频率论方法，但迄今为止还没有贝叶斯处理。在这篇文章中，我们描述了贝叶斯方法来建模一个灵活的回归函数时，预测变量的测量误差。回归函数用平滑样条和回归P样条建模。两种方法被描述为探索的后方。第一种称为迭代条件模式（ICM），只是部分贝叶斯。ICM使用分量最大化例程来找到后验的模式，它还用于为第二种方法创建起始值，第二种方法完全是贝叶斯的，并使用马尔可夫链蒙特卡罗（MCMC）技术从联合后验分布中生成观测值。使用MCMC方法的优点是，可以很容易地计算直接建模和调整测量误差的区间估计。我们提供了几个非线性回归函数的模拟，并提供了一个说明性的例子。我们的模拟表明，频率论的均方误差特性的完全贝叶斯方法是优于ICM和以前提出的频率论的方法，至少在我们已经研究的例子。
In the presence of covariate measurement error, estimating a regression function nonparametrically is extremely difficult, the problem being related to deconvolution. Various frequentist approaches exist for this problem, but to date there has been no Bayesian treatment. In this article we describe Bayesian approaches to modeling a flexible regression function when the predictor variable is measured with error. The regression function is modeled with smoothing splines and regression P-splines. Two methods are described for exploration of the posterior. The first, called the iterative conditional modes (ICM), is only partially Bayesian. ICM uses a componentwise maximization routine to find the mode of the posterior, It also serves to create starting values for the second method, which is fully Bayesian and uses Markov chain Monte Carlo (MCMC) techniques to generate observations from the joint posterior distribution. Use of tire MCMC approach has the advantage that interval estimates that directly model and adjust for the measurement error are easily calculated. We provide simulations with several nonlinear regression functions and provide an illustrative example. Our simulations indicate that the frequentist mean squared error properties of the fully Bayesian method are better than those of ICM and also of previously proposed frequentist methods, at least in the examples that we have studied.