论文标题
von Mises-Fisher分布及其统计分歧
von Mises-Fisher distributions and their statistical divergence
论文作者
论文摘要
von mises-fisher家族是单位球表面上分布的参数家族，总结了浓度参数和平均方向。作为准巴约西亚语的先验，当参数空间与超晶（例如，半参数离散选择中的最大得分估计，通过经验性的最大化估算通过经验性的最大化量估算的近距离估算，von mises-fisher分布是一个方便且简单的选择（例如，在半参数离散选择中的最大得分估计，估计单位辅助分配规则的估计，并实现固定方程。尽管有悠久的应用历史，但尚未在分析中对von mises-fisher分布进行分析表征。本文提供了von Mises-fisher分布的$ f $ didivergence的分析表达式，从$ \ Mathbb {r}^p $中的另一个独特的，von mises-fisher分布以及超透明的统一分布。本文还收集了与Von Mises-Fisher分布家族有关的其他几个结果，并表征了我们考虑的分歧度量的限制行为。
The von Mises-Fisher family is a parametric family of distributions on the surface of the unit ball, summarised by a concentration parameter and a mean direction. As a quasi-Bayesian prior, the von Mises-Fisher distribution is a convenient and parsimonious choice when parameter spaces are isomorphic to the hypersphere (e.g., maximum score estimation in semi-parametric discrete choice, estimation of single-index treatment assignment rules via empirical welfare maximisation, under-identifying linear simultaneous equation models). Despite a long history of application, measures of statistical divergence have not been analytically characterised for von Mises-Fisher distributions. This paper provides analytical expressions for the $f$-divergence of a von Mises-Fisher distribution from another, distinct, von Mises-Fisher distribution in $\mathbb{R}^p$ and the uniform distribution over the hypersphere. This paper also collect several other results pertaining to the von Mises-Fisher family of distributions, and characterises the limiting behaviour of the measures of divergence that we consider.
