  The inference of correlated signal fields with unknown correlation structures
is of high scientific and technological relevance, but poses significant
conceptual and numerical challenges. To address these, we develop the
correlated signal inference (CSI) algorithm within information field theory
(IFT) and discuss its numerical implementation. To this end, we introduce the
free energy exploration (FrEE) strategy for numerical information field theory
(NIFTy) applications. The FrEE strategy is to let the mathematical structure of
the inference problem determine the dynamics of the numerical solver. FrEE uses
the Gibbs free energy formalism for all involved unknown fields and correlation
structures without marginalization of nuisance quantities. It thereby avoids
the complexity marginalization often impose to IFT equations. FrEE
simultaneously solves for the mean and the uncertainties of signal, nuisance,
and auxiliary fields, while exploiting any analytically calculable quantity.
Finally, FrEE uses a problem specific and self-tuning exploration strategy to
swiftly identify the optimal field estimates as well as their uncertainty maps.
For all estimated fields, properly weighted posterior samples drawn from their
exact, fully non-Gaussian distributions can be generated. Here, we develop the
FrEE strategies for the CSI of a normal, a log-normal, and a Poisson log-normal
IFT signal inference problem and demonstrate their performances via their NIFTy
implementations.
