论文标题
Weyl先验和贝叶斯统计
Weyl Prior and Bayesian Statistics
论文作者
论文摘要
使用贝叶斯推理时，需要选择参数的先验分布。著名的Jeffreys先验是基于统计歧管上的Riemann度量张量。 Takeuchi和Amari定义了$α$ - 平行的先验，通过利用高阶几何对象（称为Chentsov-Amari张量），该$α$ - 平行的先验。在本文中，我们根据统计歧管上的Weyl结构提出了一个新的先验。事实证明，我们的先前是$α$ - 平行的特殊情况，其参数$α$等于$ -n $，其中$ n $是基础统计歧管的维度，而减号是$α$ - 连接定义中使用的惯例的结果。这是选择参数$α$的选择。我们计算了单变量高斯和多元高斯分布的Weyl先验。单变量高斯的先验事实证明是统一的先验。
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 higher-order geometric object, known as 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 $α$ equals $-n$, where $n$ 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.
