Topological Perspectives on Statistical Quantities II

TL;DR

This paper explores the use of topological algebraic structures, specifically $C_ inf$ algebras, to analyze cumulants in statistics, linking algebraic homotopy concepts with measures of independence.

Contribution

It introduces the concept of cumulants for $C_ inf$ morphisms, extending previous work on Boolean cumulants of $A_ inf$ morphisms to a new algebraic-topological context.

Findings

Defined cumulants for $C_ inf$ morphisms.

Connected cumulants to measures of independence.

Extended algebraic framework for statistical analysis.

Abstract

$C_\infty$ Algebras and their morphisms are a framework in which one can study algebras and their maps that are not commutaive-associative but are homotopic to being that. In statistics cumulants measure the independence of random variables. Another way of describing them would be as measure of deviation from being an algebra map. In this paper we explore the notion of cumulants of $C_\infty$ morphisms. This uses a previous analysis about Boolean cumulants of $A_\infty$ morphisms.