论文标题
在高斯orlicz-sobolev空间上建模的仿射统计捆绑包
Affine statistical bundle modeled on a Gaussian Orlicz-Sobolev space
论文作者
论文摘要
统计流形的双重平坦结构可以从在合格的一组概率度量上定义的特定仿射空间的情况下以非参数方式得出。仿射空间的统计自然位移映射取决于费舍尔分数的概念。如果状态空间不是有限的，则必须仔细定义模型空间。在各种选择中，我们讨论了如何使用高斯重量的Orlicz-Sobolev空间。这样的完全非参数设置提供了讨论本质上无限多维进化问题的工具。
The dually flat structure of statistical manifolds can be derived in a non-parametric way from a particular case of affine space defined on a qualified set of probability measures. The statistically natural displacement mapping of the affine space depends on the notion of Fisher's score. The model space must be carefully defined if the state space is not finite. Among various options, we discuss how to use Orlicz-Sobolev spaces with Gaussian weight. Such a fully non-parametric set-up provides tools to discuss intrinsically infinite-dimensional evolution problems.
