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Bayesian variable selection in linear regression models with non-normal errors

机译：具有非正态误差的线性回归模型中的贝叶斯变量选择

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摘要

This paper addresses two crucial issues in multiple linear regression analysis: (i) error terms whose distribution is non-normal because of the presence of asymmetry of the response variable and/or data coming from heterogeneous populations; (ii) selection of the regressors that effectively contribute to explaining patterns in the observations and are relevant for predicting the dependent variable. A solution to the first issue can be obtained through an approach in which the distribution of the error terms is modelled using a finite mixture of Gaussian distributions. In this paper we use this approach to specify a Bayesian linear regression model with non-normal errors; furthermore, by embedding Bayesian variable selection techniques in the specification of the model, we simultaneously perform estimation and variable selection. These tasks are accomplished by sampling from the posterior distributions associated with the model. The performances of the proposed methodology are evaluated through the analysis of simulated datasets in comparison with other approaches. The results of an analysis based on a real dataset are also provided. The methods developed in this paper result to perform well when the distribution of the error terms is characterised by heavy tails, skewness and/or multimodality.
机译：本文解决了多元线性回归分析中的两个关键问题：（i）由于响应变量和/或来自异类总体的数据的不对称性，其误差分布非正态的误差项； （ii）选择有效地有助于解释观测模式并与预测因变量相关的回归变量。通过使用高斯分布的有限混合对误差项的分布进行建模的方法，可以获得第一个问题的解决方案。在本文中，我们使用这种方法来指定具有非正态误差的贝叶斯线性回归模型。此外，通过将贝叶斯变量选择技术嵌入模型的规范中，我们可以同时执行估计和变量选择。这些任务是通过从与模型关联的后验分布中采样来完成的。通过与其他方法比较分析模拟数据集来评估所提出方法的性能。还提供了基于真实数据集的分析结果。当误差项的分布以重尾，偏斜和/或多模态为特征时，本文开发的方法可以很好地执行。

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