Integral equation solutions as prior distributions for Bayesian model selection
Integral equation solutions as prior distributions for Bayesian model selection
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DOI：
10.1007/s11749-006-0040-8
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发表时间：
2008-11-01
期刊：
影响因子：
1.3
通讯作者：
Robert, C. P.
中科院分区：
文献类型：
--
作者：
Cano, J. A.;Salmeron, D.;Robert, C. P.
在许多统计问题中，我们处理不止一个模型。当模型参数的先验信息模糊时，通常使用默认先验。不幸的是，这些先验通常是不适当的挑起校准问题，这排除了模型的比较。解决这一困难的尝试包括使用内在先验，在Berger和Pericchi（1996，The intrinsic Bayes factor for model selection and prediction. J Am Stat Asynchronous 91：109-122），而不是原来的默认先验;然而，也有情况下，类的内在先验太大。因为这一点，我们提出的先验分布模型选择是一个系统的积分方程的解决方案，导出校准初始默认先验。在某些假设下，我们的积分方程产生唯一的解。提供了一些说明性的例子。
In many statistical problems we deal with more than one model. When the prior information on the parameters of the models is vague default priors are typically used. Unfortunately, these priors are usually improper provoking a calibration problem which precludes the comparison of the models. An attempt for solving this difficulty consists in using intrinsic priors, introduced in Berger and Pericchi (1996, The intrinsic Bayes factor for model selection and prediction. J Am Stat Assoc 91:109-122), instead of the original default priors; however, there are situations where the class of intrinsic priors is too large.Because of this we propose prior distributions for model selection that are solutions of a system of integral equations which is derived to calibrate the initial default priors. Under some assumptions our integral equations yield a unique solution. Some illustrative examples are provided.