Operator Calculus for Information Field Theory

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.