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A Bayesian Approach to Inverse Quantum Statistics

J. C. Lemm·J. Uhlig·A. Weiguny
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Abstract

A nonparametric Bayesian approach is developed to determine quantum potentials from empirical data for quantum systems at finite temperature. The approach combines the likelihood model of quantum mechanics with a priori information over potentials implemented in form of stochastic processes. Its specific advantages are the possibilities to deal with heterogeneous data and to express a priori information explicitly, i.e., directly in terms of the potential of interest. A numerical solution in maximum a posteriori approximation was feasible for one--dimensional problems. Using correct a priori information turned out to be essential.

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J. C. Lemm, J. Uhlig, A. Weiguny. 1999-07-01. A Bayesian Approach to Inverse Quantum Statistics. https://doi.org/10.1103/physrevlett.84.2068

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