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Bayesian analysis of some models that use the asymmetric exponential power distribution

机译：使用非对称指数幂分布的某些模型的贝叶斯分析

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The asymmetric exponential power (AEP) family includes the symmetric exponential power distribution as a particular case. It provides flexible distributions with lighter and heavier tails compared to the normal one. The distributions of this family can successfully handle both symmetry/asymmetry and light/heavy tails simultaneously. Even more, the distributions can fit each tail separately. This provides a great flexibility when fitting experimental data. The idea of using a scale mixture of uniform representation of the AEP distribution is exploited to derive efficient Gibbs sampling algorithms in three different Bayesian contexts. Firstly, a posterior exploration is performed, where the AEP distribution is considered for the likelihood model. Secondly, a linear regression model, that uses the AEP distribution for the error variable, is developed. And finally, a binary regression model is analyzed, by using the inverse of the AEP cumulative distribution function as the link function. These three models have been built in such a way that they share some full conditional distributions to sample from their respective posterior distributions. The theoretical results are illustrated by comparing with other competing models using some previously published datasets.
机译：作为特殊情况，非对称指数幂（AEP）系列包括对称指数幂分布。与普通尾巴相比，它具有灵活的分布，尾巴更轻，更重。该族的分布可以成功地同时处理对称/不对称和轻/重尾巴。更重要的是，分布可以分别适合每条尾巴。在拟合实验数据时，这提供了极大的灵活性。利用AEP分布的均匀表示的比例混合的想法，可以在三种不同的贝叶斯环境中得出有效的吉布斯采样算法。首先，进行后验探索，其中对似然模型考虑AEP分布。其次，建立了使用误差变量的AEP分布的线性回归模型。最后，通过使用AEP累积分布函数的逆函数作为链接函数来分析二元回归模型。建立这三个模型的方式是，它们共享一些完整的条件分布以从各自的后验分布中进行采样。通过使用一些以前发布的数据集与其他竞争模型进行比较来说明理论结果。

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