This work introduces a novel methodology based on finite mixtures of Student-t distributions to model the errors' distribution in linear regression models. The novelty lies on a particular hierarchical structure for the mixture distribution in which the first level models the number of modes, responsible to accommodate multimodality and skewness features, and the second level models tail behaviour. Moreover, the latter is specified in a way that no estimation of the degrees of freedom parameters is required. This way, the known statistical difficulties when dealing with those parameters are mitigated and yet model flexibility is not compromised. The inference is performed via a carefully designed Markov chain Monte Carlo algorithm and simulation studies are conducted to evaluate the performance of the proposed methodology. The analysis of two real data sets is also presented.

中文翻译：

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具有灵活误差分布的贝叶斯线性回归模型

这项工作引入了一种基于 Student-t 分布的有限混合的新方法，以对线性回归模型中的误差分布进行建模。新颖之处在于混合分布的特定层次结构，其中第一级对模式数量进行建模，负责适应多模态和偏度特征，第二级对尾部行为进行建模。此外，后者是以不需要估计自由度参数的方式指定的。这样，在处理这些参数时已知的统计困难得到了缓解，而且模型的灵活性不会受到影响。推理是通过精心设计的马尔可夫链蒙特卡罗算法进行的，并进行了模拟研究以评估所提出方法的性能。