Robust Recursive Bayesian Estimation and Quantum Minimax Strategies

The problem of a recursive realization of Bayesian estimation for incomplete experimental data is considered. A differential-geometric structure of nonlinear estimation is studied. It is shown that the use of a rationally chosen description of the true posterior density produces a geometrical structure defined on the family of possible posteriors. Pythagorean-like relations valid for probability distributions are presented and their importance for estimation under reduced data is indicated. A robust algorithm for estimation of unknown parameters is proposed, which is based on a quantum implementation of the Bayesian estimation procedure.