Bayesian estimation and inference for generalised partial linear models using shape-restricted splines-猫眼课题宝

使用形状限制样条的广义部分线性模型的贝叶斯估计和推理

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发表时间：

2011

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作者：

Mary C. Meyer;A. Hackstadt;J. Hoeting

提出了一种推广的部分线性回归模型的贝叶斯方法，其中回归函数是在形状和光滑性的假设下，使用回归样条非参数建模的。节点可以被建模为固定的或自由的，结合了用于后者的可逆跳跃马尔可夫链蒙特卡罗算法。与其他贝叶斯约束光滑器相比，模糊先验分布的建模框架提供了更多的灵活性；此外，该方法更简单、更直观、更易于实现，并且计算速度更快。关于参数模型协变量的推断可以使用近似边缘分布来完成，使用标准的贝叶斯模型选择方法来进行更一般的推断。仿真结果表明，该推理方法具有良好的贝叶斯和频域特性。特别是，当满足参数假设时，这些方法的性能通常与标准参数方法相似，而当假设被违反时，这些方法的性能优于标准参数方法。实现这里描述的方法的R代码可以在www.stat.colstate.edu/~meyer/code.htm上找到。

A Bayesian approach to generalised partial linear regression models is proposed, where regression functions are modelled nonparametrically using regression splines, with assumptions about shape and smoothness. The knots may be modelled as fixed or free, incorporating a reversible-jump Markov chain Monte Carlo algorithm for the latter. The modelling framework along with vague prior distributions provides more flexibility compared with other Bayesian constrained smoothers; further, the method is simpler, more intuitive, easier to implement, and computationally faster. Inference concerning parametrically modelled covariates can be accomplished using approximate marginal distributions, with standard Bayes model selection methods for more general inference. Simulations show that the inference methods have desirable Bayesian and frequentist properties. In particular, these methods often perform similarly to standard parametric methods when the parametric assumptions are met and are superior when the assumptions are violated. The R code to implement the methods described here is available at www.stat.colostate.edu/~meyer/code.htm.

On Bayesian analysis of mixtures with an unknown number of components. Discussion. Author's reply

DOI： --

发表时间： 1997

期刊：

Journal of the royal statistical society series b-methodological

影响因子： --

作者：

S. Richardson;P. Green;Christian P. Robert;M. Aitkin;David R. Cox;Matthew Stephens;A. Polymenis;W. Gilks;A. Nobile;M. Hodgson;Anthony O'Hagan;N. Longford;A. Dawid;Anthony C. Atkinson;J. Bernardo;J. Besag;Stephen Brooks;S. Byers;A. Raftery;G. Celeux;R. Cheng;W. B. Liu;Yung-Hsin Chien;Edward I. George;N. Cressie;H.-C. Huang;M. Gruet;S. C. Heath;C. Jennison;Andrew B. Lawson;Allan Clark;Geoffrey J. McLachlan;D. Peel;K. Mengersen;A. George;Anne Philippe;Kathryn Roeder;Larry Wasserman;Peter Schlattmann;D. Böhning;D. M. Titterington;H. Tong;M. West

通讯作者：

Bayesian estimation and inference for generalised partial linear models using shape-restricted splines

使用形状限制样条的广义部分线性模型的贝叶斯估计和推理

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