Bayesian approach to inverse quantum statistics

A nonparametric Bayesian approach is developed to determine quantum potenti als from empirical data for quantum systems at finite temperature. The appr oach combines the likelihood model of quantum mechanics with a priori infor mation on potentials implemented in the form of stochastic processes. Its s pecific advantages are the possibilities to deal with heterogeneous data an d to express a priori information explicitly in terms of the potential of i nterest. A numerical solution in maximum a posteriori approximation is obta ined for one-dimensional problems. As nonparametric estimates, the results depend strongly on the implemented a priori information.