It is argued from several points of view that quantum probabilities might play a role in statistical settings. New approaches toward quantum foundations have postulates that appear to be equally valid in macroscopic settings. One such approach is described here in detail, while one other is briefly sketched. In particular, arguments behind the Born rule, which gives the basis for quantum probabilities, are given. A list of ideas for possible statistical applications of quantum probabilities is provided and discussed. A particular area is machine learning, where there exists substantial literature on links to quantum probability. Here, an idea about model reduction is sketched and is motivated from a quantum probability model. Quantum models can play a role in model reduction, where the partial least squares regression model is a special case. It is shown that for certain experiments, a Bayesian prior given by a quantum probability can be motivated.
Quantum probability for statisticians; some new ideas
It is vital to build bridges between various scientific communities. This paper is the end product on a long process, which includes: 1) several papers in physics journals, the latest one in J. Math. Phys. ; 2) a discussion paper in SJS; 3) a book to appear: On God, Complementarity, and Decisions.