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Updated: Jan 19, 2026

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Hilbert space multidimensional modelling of continuous measurements.

J R Busemeyer1, Z Wang2

  • 1Indiana University, Bloomington, IN, USA.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|September 17, 2019
PubMed
Summary

This study introduces a Hilbert space multidimensional theory to address data fusion challenges arising from different measurement contexts. The novel approach uses state vectors and measurement operators to accurately model context effects in empirical data analysis.

Keywords:
Kolmogorov probabilitycontext effectsquantum probability

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Area of Science:

  • Quantum mechanics
  • Probability theory
  • Data analysis

Background:

  • Data fusion problems occur when analyzing empirical data from varied measurement contexts.
  • A context effect arises when distributions from different contexts cannot be reconciled with a complete joint distribution.
  • Existing methods struggle to reconcile context-dependent data distributions.

Purpose of the Study:

  • To propose a novel theoretical framework for addressing data fusion problems.
  • To develop a method capable of accounting for context effects in empirical data.
  • To provide a mathematical model for analyzing data from multiple measurement contexts.

Main Methods:

  • A Hilbert space multidimensional theory is proposed.
  • The theory utilizes state vectors and measurement operators.
  • This framework models multiple distributions arising from different contexts.

Main Results:

  • The proposed theory successfully accounts for multiple distributions generated by different contexts.
  • It provides a method to analyze data where context effects are present.
  • The framework offers a way to overcome limitations of marginalizing over joint distributions.

Conclusions:

  • The Hilbert space multidimensional theory offers a robust solution for data fusion challenges.
  • This approach effectively models and analyzes context effects in empirical data.
  • The findings contribute to understanding contextuality and probability in quantum mechanics and beyond.