Statistical Methods in Quantum Theory

Efim S. Fradkin, Igor Anatol'evich Batalin, G. A. Vilkovisky +1 more

Edward G. Harris

Shiro Ishikawa

Since the problem: "What is statistics?" is most fundamental in sceince, in order to solve this problem, there is every reason to believe that we have to start from the proposal of a worldview. Recently we proposed measurement theory (i.e., quantum language, or the linguistic interpretation of quantum mechanics), which is characterized as the linguistic turn of the Copenhagen interpretation of quantum mechanics. This turn from physics to language does not only extend quantum theory to classical theory but also yield the quantum mechanical world view (i.e., the (quantum) linguistic world view, and thus, a form of quantum thinking, in other words, quantum philosophy). Thus, we believe that the quantum lingistic formulation of statistics gives an answer to the question: "What is statistics?". In this paper, this will be done through the studies of inference interval, statistical hypothesis testing, Fisher maximum likelihood method, Bayes method and regression analysis in meaurement theory.

Inge Svein Helland

The Basic Elements Statistical Theory and Practice Statistical Inference Under Symmetry The Transition from Statistics to Quantum Theory Quantum Mechanics from a Statistical Basis Further Development of Quantum Mechanics Decisions in Statistics Multivariate Data Analysis and Statistics Quantum Mechanics and the Diversity of Concepts.

Wesley E. Brittin, Asım Orhan Barut