Wave-function parametrization of a probability measure

Abstract

We show that the unitary operator on a separable Hilbert space is a parametrization of any conditional probability measure in a standard measure space. We propose unitary inference, a generalization of Bayesian inference. We study implications for classical statistical mechanics.

18 pages, v4: An error (without major consequences) in section 3 was corrected. Direct sum of linear models with few variables (aka Renormalization) discussed