Affine statistical bundle modeled on a Gaussian Orlicz-Sobolev space

TL;DR

This paper develops a non-parametric affine statistical model using Gaussian Orlicz-Sobolev spaces, enabling analysis of infinite-dimensional evolution problems in statistical manifolds.

Contribution

It introduces a novel affine statistical bundle framework based on Gaussian Orlicz-Sobolev spaces for non-parametric, infinite-dimensional statistical analysis.

Findings

Constructs a non-parametric affine statistical model on Gaussian Orlicz-Sobolev spaces.

Provides tools for analyzing infinite-dimensional evolution problems.

Discusses the geometric structure of statistical manifolds beyond finite dimensions.

Abstract

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.