Mixtures of shifted asymmetric Laplace distributions were introduced as a tool for model-based clustering that allowed for the direct parameterization of skewness in addition to location and scale. Following common practices, an expectation-maximization algorithm was developed to fit these mixtures. However, adaptations to account for the `infinite likelihood problem' led to fits that gave good classification performance at the expense of parameter recovery. In this paper, we propose a more valuable solution to this problem by developing a novel Bayesian parameter estimation scheme for mixtures of shifted asymmetric Laplace distributions. Through simulation studies, we show that the proposed parameter estimation scheme gives better parameter estimates compared to the expectation-maximization based scheme. In addition, we also show that the classification performance is as good, and in some cases better, than the expectation-maximization based scheme. The performance of both schemes are also assessed using well-known real data sets.

翻译：混合平移异态拉普拉斯分布被引入作为一种基于模型的聚类工具，允许直接对偏态进行参数化，同时考虑位置和尺度。按照常见做法，我们开发了一个期望最大化算法来拟合这些混合模型。但是，针对“无限似然问题”的改进导致拟合结果在分类性能方面表现良好，但在参数恢复方面表现出问题。在本文中，我们提出了一种更有价值的解决方案，即为混合平移异态拉普拉斯分布开发一种新颖的贝叶斯参数估计方案。通过模拟研究，我们展示了所提出的参数估计方案相较于期望最大化方案提供更好的参数估计。此外，我们还展示了两种方案的分类性能相当好，甚至在某些情况下更好。两种方案的性能也使用了众所周知的真实数据集进行了评估。