A quantum framework for likelihood ratios
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 assumptionfree 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 expectationmaximization techniques. This paper takes an informationtheoretic 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.
 Publication:

International Journal of Quantum Information
 Pub Date:
 2018
 DOI:
 10.1142/S0219749918500028
 arXiv:
 arXiv:1508.00936
 Bibcode:
 2018IJQI...1650002B
 Keywords:

 Bayes’ theorem;
 probability;
 statistics;
 inference;
 decisionmaking;
 Mathematics  Statistics Theory;
 High Energy Physics  Theory;
 Quantum Physics
 EPrint:
 doi:10.1142/S0219749918500028