Partition function approach to non-Gaussian likelihoods: Partitions for the inference of functions and the Fisher-functional

Abstract

Motivated by constraints on the dark energy equation of state from a data set of supernova distance moduli, we propose a formalism for the Bayesian inference of functions: Starting at a functional variant of the Kullback-Leibler divergence we construct a functional Fisher-matrix and a suitable partition functional which takes on the shape of a path integral. After showing the validity of the CramCrossed D sign