We study logarithmic Voronoi cells for linear statistical models and partial linear models. The logarithmic Voronoi cells at points on such model are polytopes. To any $d$-dimensional linear model inside the probability simplex $\Delta_{n-1}$, we can associate an $n\times d$ matrix $B$. For interior points, we describe the vertices of these polytopes in terms of co-circuits of $B$. We also show that these polytopes are combinatorially isomorphic to the dual of a vector configuration with Gale diagram $B$. This means that logarithmic Voronoi cells at all interior points on a linear model have the same combinatorial type. We also describe logarithmic Voronoi cells at points on the boundary of the simplex. Finally, we study logarithmic Voronoi cells of partial linear models, where the points on the boundary of the model are especially of interest.
翻译:我们研究线性统计模型和部分线性模型的对数Voronoi细胞。在这种模型的点上的对数Voronoi细胞是多面体。对于在概率简单x$\Delta ⁇ n-1}$范围内的任何美元维线性模型,我们可以将一个美元乘数dmex d$B$。对于内部点,我们用双向电路用$B$来描述这些多面体的顶端。我们还表明,这些多面体是组合式的异形,与加勒图的矢量配置的双向。这意味着,线性模型所有内点的对数Vorononoi细胞都有相同的组合类型。我们还描述了在简单x边界点的对数Voronoioi细胞。最后,我们研究了部分线性模型的对数细胞,而模型的边界点特别感兴趣。