Quantum mechanical view of mathematical statistics

Yu. I. Bogdanov

doi:10.1117/12.683116

31 May 2006 Quantum mechanical view of mathematical statistics

Yu. I. Bogdanov

Proceedings Volume 6264, Quantum Informatics 2005; 62640E (2006) https://doi.org/10.1117/12.683116
Event: Quantum Informatics 2005, 2005, Moscow, Russian Federation

Abstract

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. A new statistical characteristic, a confidence cone, is introduced instead of a standard confidence interval. The chi-square test is considered to test the hypotheses that the estimated vector converges to the state vector of a general population and that both samples are homogeneous. The expansion coefficients are estimated by the maximum likelihood method. An iteration algorithm for solving the likelihood equation is presented. The stability and rate of convergence of the solution are studied. A special iteration parameter is introduced: its optimal value is chosen on the basis of the maximin strategy. Numerical simulation is performed using the set of the Chebyshev-Hermite functions as a basis.

Citation Download Citation

Yu. I. Bogdanov "Quantum mechanical view of mathematical statistics", Proc. SPIE 6264, Quantum Informatics 2005, 62640E (31 May 2006); https://doi.org/10.1117/12.683116

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KEYWORDS

Statistical analysis

Quantum mechanics

Numerical simulations

Data analysis

Quantum physics

Error analysis

Probability theory

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