This paper is meant to introduce a significant extension of the flexible Dirichlet (FD) distribution, which is a quite tractable special mixture model for compositional data, i.e. data representing vectors of proportions of a whole. The FD model displays several theoretical properties which make it suitable for inference, and fairly easy to handle from a computational viewpoint. However, the rigid type of mixture structure implied by the FD makes it unsuitable to describe many compositional datasets. Furthermore, the FD only allows for negative correlations. The new extended model, by considerably relaxing the strict constraints among clusters entailed by the FD, allows for a more general dependence structure (including positive correlations) and greatly expands its applicative potential. At the same time, it retains, to a large extent, its good properties. EM-type estimation procedures can be developed for this more complex model, including ad hoc reliable initialization methods, which permit to keep the computational issues at a rather uncomplicated level. Accurate evaluation of standard error estimates can be provided as well.

中文翻译：

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单纯形上的新混合模型

本文旨在介绍可扩展的Dirichlet（FD）分布的显着扩展，它是组成数据（即表示整体比例矢量的数据）非常易于处理的特殊混合模型。FD模型显示了一些理论上的属性，使其适用于推理，并且从计算角度来看很容易处理。但是，FD暗示的混合结构的刚性类型使其不适用于描述许多成分数据集。此外，FD仅允许负相关。新的扩展模型通过极大地放松了FD所引起的集群之间的严格约束，从而实现了更一般的依赖结构（包括正相关），并极大地扩展了其应用潜力。同时，它在很大程度上保留了 其良好的性能。可以为这种更复杂的模型开发EM类型的估计程序，包括临时可靠的初始化方法，该方法可以将计算问题保持在相当简单的水平上。也可以提供标准误差估计值的准确评估。