A new method for multinomial inference is proposed by representing the cell probabilities as unordered segments on the unit interval and following Dempster-Shafer (DS) theory. The resulting DS posterior is then strengthened to improve symmetry and learning properties with the final posterior model being characterized by a Dirichlet distribution. In addition to computational simplicity, the new model has desirable invariance properties related to category permutations, refinements, and coarsenings. Furthermore, posterior inference on relative probabilities amongst certain cells depends only on data for the cells in question. Finally, the model is quite flexible with regard to parameterization and the range of testable assertions. Comparisons are made to existing methods and illustrated with two examples.

翻译：本文提出了一种新的多项推断方法，其核心思想是将单元概率表示为单位区间上的无序分段，并遵循Dempster-Shafer（DS）理论。随后对所得的DS后验进行强化，以改善对称性和学习特性，最终的后验模型以狄利克雷分布为特征。该新模型除了计算简便外，还具有关于类别置换、细化和粗化的理想不变性。此外，对特定单元间相对概率的后验推断仅依赖于相关单元的数据。最后，该模型在参数化和可检验断言的范围方面具有高度灵活性。本文与现有方法进行了比较，并通过两个示例加以说明。