A quantum framework for likelihood ratios

Bond, Rachael L, He, Yang-Hui and Ormerod, Thomas C (2017) A quantum framework for likelihood ratios. International Journal of Quantum Information, 16 (1). ISSN 0219-7499

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Abstract

The ability to calculate precise likelihood ratios is fundamental to science, from Quantum Information Theory through to Quantum State Estimation. However, there is no assumption-free statistical methodology to achieve this. For instance, in the absence of data relating to covariate overlap, the widely used Bayes' theorem either defaults to the marginal probability driven "naive Bayes' classifier", or requires the use of compensatory expectation-maximization techniques. This article takes an information-theoretic approach in developing a new statistical formula for the calculation of likelihood ratios based on the principles of quantum entanglement, and demonstrates that Bayes' theorem is a special case of a more general quantum mechanical expression.

Item Type: Article
Keywords: Bayes' theorem, Inference, Decision making, Statistics
Schools and Departments: School of Psychology > Psychology
Subjects: Q Science > QA Mathematics > QA0273 Probabilities. Mathematical statistics
Q Science > QA Mathematics > QA0276 Mathematical statistics
Q Science > QC Physics > QC0170 Atomic physics. Constitution and properties of matter Including molecular physics, relativity, quantum theory, and solid state physics
Q Science > QZ Psychology
Depositing User: Rachael Louise Bond
Date Deposited: 20 Nov 2017 08:30
Last Modified: 12 Dec 2017 12:33
URI: http://sro.sussex.ac.uk/id/eprint/71402

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