Stochastic factorizations, sandwiched simplices and the topology of the space of explanations
Stochastic factorizations, sandwiched simplices and the topology of the space of explanations
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随机因式分解、夹层单纯形和解释空间的拓扑
DOI：
10.1098/rspa.2003.1150
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发表时间：
2003
期刊：
影响因子：
--
通讯作者：
Duco van Straten
中科院分区：
文献类型：
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作者：
D. Mond;Jim T. Smith;Duco van Straten
我们研究随机矩阵 V 的随机分解空间，其动机是隐藏随机变量的统计问题。我们证明这个空间与夹在两个嵌套凸多面体之间的单纯形空间是同胚的，并使用这个几何模型来深入了解它的结构和拓扑。我们证明了描述其同伦类型的定理，并且在 V 的秩为 2 的情况下，我们给出了完整的描述，包括连通分量数量的界限以及达到这些界限的示例。我们试图让统计学家能够理解并关联拓扑的概念。
We study the space of stochastic factorizations of a stochastic matrix V, motivated by the statistical problem of hidden random variables. We show that this space is homeomorphic to the space of simplices sandwiched between two nested convex polyhedra, and use this geometrical model to gain some insight into its structure and topology. We prove theorems describing its homotopy type, and, in the case where the rank of V is 2, we give a complete description, including bounds on the number of connected components, and examples in which these bounds are attained. We attempt to make the notions of topology accessible and relevant to statisticians.