论文标题
提升统计结构
Lifting statistical structures
论文作者
论文摘要
我们考虑与统计流形（度量张量，双重连接，偏度张量等）相关的几何对象的一些自然（功能）升力。事实证明，抬起的对象再次形成统计歧管结构，这次是在较高的切线束上，唯一的区别是公制张量是伪riemannian。更重要的是，电势的自然提升（也称为差异或对比功能）再次成为电势，这次是提升的统计结构。我们提出了一个类似的程序，用于在谎言代数上提升统计结构，并提出在lie gropoid上定义的对比函数。特别是，我们详细研究了较高的li子类固定束的li子类固定结构。我们通过明确的例子说明了提升的几何构造，包括一些重要的统计模型和lie lie类的潜在功能。
We consider some natural (functorial) lifts of geometric objects associated with statistical manifolds (metric tensor, dual connections, skewness tensor, etc.) to higher tangent bundles. It turns out that the lifted objects form again a statistical manifold structure, this time on the higher tangent bundles, with the only difference that the metric tensor is pseudo-Riemannian. What is more, natural lifts of potentials (called also divergence or contrast functions) turn out to be again potentials, this time for the lifted statistical structures. We propose an analogous procedure for lifting statistical structures on Lie algebroids and lifting contrast functions which are defined on Lie groupoids. In particular, we study in detail Lie groupoid structures of higher tangent bundles of Lie groupoids. Our geometric constructions of lifts are illustrated by explicit examples, including some important statistical models and potential functions on Lie groupoids.
