Bayes Factors for Outlier Models Using the Device of Imaginary Observations
利用虚拟观测构造异常值模型的贝叶斯因子AI 解读 ↓
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利用虚拟观测构造异常值模型的贝叶斯因子
- 研究问题
- 在异常值污染参数缺乏可靠先验信息时，如何使用非正常先验比较无异常值与含异常值的候选模型？
- 方法与思路
- 作者通过虚拟训练样本确定污染分布参数的非正常先验常数，计算模型间的贝叶斯因子，并扩展至多个异常值。
- 材料陈述的贡献
- 摘要称，这一构造支持异常值模型比较，并在单变量正态分布、简单线性回归和指数样本中给出方法示例。
- 阅读关注点
- 应核对虚拟训练样本如何选择、先验常数如何确定，以及贝叶斯因子对训练样本和污染模型设定的敏感性。
- 阅读边界
- 摘要未说明训练样本的具体规则、唯一性或稳健性，不能认定已普遍解决异常值识别；索引稿件版本及刊本变化未知。
原文摘要
Suppose we think that most observations in a sample have been generated from a distribution with density f(x) but we fear that a few outliers from a distribution with density g(x) may have contaminated our sample. In many situations, we might assume that f(x) is a density depending on a parameter θ and that g(x) is of the same form as f but with parameter θ + δ or θδ. A number of Bayesian models for this problem when f is normal have been discussed by Freeman. He points out that with a vague improper prior for contaminating parameters, most posterior weight is put on the model allowing for the largest number of outliers. He therefore confines attention to proper priors when trying to answer the question of “how many outliers?” However, in many situations we do not have very certain information on the contaminating parameters and would like to make inferences about outliers when using improper priors for the parameters of the model. In this article, we apply the ideas of Spiegelhalter and Smith to this problem. In particular, we use their idea of assigning the value of the constant in the improper prior for the parameter of the contaminating distribution by the device of an imaginary training sample. This enables us to calculate the Bayes factor comparing a model with no outliers to a model with one outlier. We also can extend the ideas to more than one outlier. We illustrate the method in the case of univariate normal distributions, simple linear regression, and exponential samples.