Quantum Mechanical View of Mathematical Statistics

Details Quantum Mechanical View of Mathematical Statistics Quantum Mechanical View of Mathematical Statistics

2003-03-03

arxiv.org/abs/quant-ph/0303013v1

Physics

Quantum Physics

OAO "Angstrem", Moscow, Russia 26 pages, 2 figure

Scientific paper

Multiparametric statistical model providing stable reconstruction of parameters by observations is considered. The only general method of this kind is the root model based on the representation of the probability density as a squared absolute value of a certain function, which is referred to as a psi function in analogy with quantum mechanics. The psi function is represented by an expansion in terms of an orthonormal set of functions. It is shown that the introduction of the psi function allows one to represent the Fisher information matrix as well as statistical properties of the estimator of the state vector (state estimator) in simple analytical forms.

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