Monotone invariants and embeddings of statistical manifolds

2005/06/09 by H. Carl Le, Le, Hong-Van
Physics and Astronomy · #53C42 #60D05 #65H20 #Differential Geometry (math.DG) #FOS: Mathematics #Statistical Mechanics and Entropy #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.math/0506163

openalex publication_date 2005/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note we prove certain necessary and sufficient conditions for the existence of an embedding of statistical manifolds. In particular, we prove that any compact smooth (C¹ resp.) statistical manifold can be embedded into the space of probability measures on a finite set. As a result, we get an answer to the Lauritzen question on a realization of smooth (C¹ resp.) statistical manifolds as statistical models

Related

• The Bonnet theorem for statistical manifolds
• Immersions into Statistical Manifolds
• Foundations of Structural Statistics: Statistical Manifolds
• Manifolds of Differentiable Densities
• Principal bundles over statistical manifolds