What is Statistics?; The Answer by Quantum Language

TL;DR

This paper explores the nature of statistics through the lens of quantum language, proposing a linguistic interpretation rooted in measurement theory to redefine statistical concepts.

Contribution

It introduces a quantum linguistic framework for statistics, extending traditional theories and providing a new philosophical perspective on statistical inference.

Findings

Quantum language offers a new foundation for statistics.

Reinterpretation of classical statistical methods in measurement theory.

Potential for a unified philosophical approach to statistical inference.

Abstract

Since the problem: "What is statistics?" is most fundamental in sceince, in order to solve this problem, there is every reason to believe that we have to start from the proposal of a worldview. Recently we proposed measurement theory (i.e., quantum language, or the linguistic interpretation of quantum mechanics), which is characterized as the linguistic turn of the Copenhagen interpretation of quantum mechanics. This turn from physics to language does not only extend quantum theory to classical theory but also yield the quantum mechanical world view (i.e., the (quantum) linguistic world view, and thus, a form of quantum thinking, in other words, quantum philosophy). Thus, we believe that the quantum lingistic formulation of statistics gives an answer to the question: "What is statistics?". In this paper, this will be done through the studies of inference interval, statistical hypothesis testing, Fisher maximum likelihood method, Bayes method and regression analysis in meaurement theory.