Jiang Ruichao, Tavakoli Javad, Zhao Yiqiang
Department of Mathematics, The University of British Columbia Okanagan, Kelowna, BC V1V 1V7, Canada.
School of Mathematics and Statistics, Carlton University, Ottawa, ON K1S 5B6, Canada.
Entropy (Basel). 2020 Apr 20;22(4):467. doi: 10.3390/e22040467.
When using Bayesian inference, one needs to choose a prior distribution for parameters. The well-known Jeffreys prior is based on the Riemann metric tensor on a statistical manifold. Takeuchi and Amari defined the α -parallel prior, which generalized the Jeffreys prior by exploiting a higher-order geometric object, known as a Chentsov-Amari tensor. In this paper, we propose a new prior based on the Weyl structure on a statistical manifold. It turns out that our prior is a special case of the α -parallel prior with the parameter α equaling - n , where is the dimension of the underlying statistical manifold and the minus sign is a result of conventions used in the definition of α -connections. This makes the choice for the parameter α more canonical. We calculated the Weyl prior for univariate Gaussian and multivariate Gaussian distribution. The Weyl prior of the univariate Gaussian turns out to be the uniform prior.
在使用贝叶斯推理时，需要为参数选择一个先验分布。著名的杰弗里斯先验是基于统计流形上的黎曼度量张量。竹内和天马里定义了α -平行先验，它通过利用一个称为陈采夫-天马里张量的高阶几何对象推广了杰弗里斯先验。在本文中，我们基于统计流形上的外尔结构提出了一种新的先验。结果表明，我们的先验是α -平行先验的一种特殊情况，其中参数α等于 - n，这里n是基础统计流形的维度，负号是α -联络定义中所采用约定的结果。这使得参数α的选择更加规范。我们计算了单变量高斯分布和多变量高斯分布的外尔先验。单变量高斯分布的外尔先验结果是均匀先验。
