Operator Calculus for Information Field Theory
Abstract
Signal inference problems with non-Gaussian posteriors can be hard to tackle. Through using the concept of Gibbs free energy these posteriors are rephrased as Gaussian posteriors for the price of computing various expectation values with respect to a Gaussian distribution. We present a new way of translating these expectation values to a language of operators which is similar to that in quantum mechanics. This simplifies many calculations, for instance such involving log-normal priors. The operator calculus is illustrated by deriving a novel self-calibrating algorithm which is tested with mock data.
Cite
@article{arxiv.1605.00660,
title = {Operator Calculus for Information Field Theory},
author = {Reimar H. Leike and Torsten A. Enßlin},
journal= {arXiv preprint arXiv:1605.00660},
year = {2016}
}
Comments
In this version there is a numerical example which demonstrates that the derived algorithm works. The paper was restructured such that it is better readable