Bell correlations outside physics

Area of Science:

• Interdisciplinary statistical analysis
• Quantum mechanics and finance

Background:

• Correlations are fundamental in science, with John Bell's framework crucial for analyzing quantum systems.
• Bell's framework, used to demonstrate non-classical quantum behavior, has broad potential applications beyond physics.

Purpose of the Study:

• To demonstrate a novel Bell-inspired approach for analyzing correlations by decomposing them into causal and noise components.
• To introduce a new measure of association and Bell-type tests applicable across disciplines.
• To highlight the general applicability of Bell's framework and statistical models in analyzing associations.

Main Methods:

• Applied a Bell-type framework to financial data (security price changes).
• Decomposed correlations into a component attributed to common causes and a component attributed to noise.
• Developed streamlined Bell-type tests for established association models like Factor Models and the bivariate Gaussian model.

Main Results:

• Introduced a new, causality-informed measure of association.
• Demonstrated the efficacy of Bell-type tests for evaluating widely used association models.
• Showcased the applicability of the proposed framework and models to financial data and general statistical analysis.

Conclusions:

• Bell's framework and associated statistical models offer general techniques for analyzing associations, transcending specific scientific domains.
• The approach provides a method to distinguish between correlations driven by genuine causes and those arising from noise.
• This work facilitates a deeper understanding of association structures and their analysis in diverse fields.