# Information-geometrical characterization of statistical models which are statistically equivalent to probability simplexes

## TL;DR

This paper characterizes statistical models equivalent to probability simplexes using information geometry concepts like alpha-families and connections, deepening understanding of their geometric structure.

## Contribution

It provides a geometric characterization of models equivalent to probability simplexes via alpha-families and related information geometric structures.

## Key findings

- Characterization of models equivalent to probability simplexes
- Connection to alpha-families, exponential, and mixture families
- Insights into alpha-connections and autoparallelity in information geometry

## Abstract

The probability simplex is the set of all probability distributions on a finite set and is the most fundamental object in the finite probability theory. In this paper we give a characterization of statistical models on finite sets which are statistically equivalent to probability simplexes in terms of $\alpha$-families including exponential families and mixture families. The subject has a close relation to some fundamental aspects of information geometry such as $\alpha$-connections and autoparallelity.