2023/06/29 by Rebecca Maria Kuntz, Kuntz, Rebecca Maria, Maximilian Philipp Herzog +7
Mathematics · Physics and Astronomy · #Cosmology and Nongalactic Astrophysics (astro-ph.CO) #Data Analysis #FOS: Physical sciences #Instrumentation and Methods for Astrophysics (astro-ph.IM) #Statistical Mechanics and Entropy #Statistical Methods and Inference #Statistical and numerical algorithms #Statistics and Probability (physics.data-an)
paper · pdf · doi:10.48550/arxiv.2306.17224
openalex publication_date 2023/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
Motivated by constraints on the dark energy equation of state from supernova-data, 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 Cramér-Rao bound and unbiasedness for functional inference in the Gaussian case, we construct Fisher-functionals for the dark energy equation of state constrained by the cosmological redshift-luminosity relationship of supernovae of type Ia, for both the linearised and the lowest-order non-linear model. Introducing Fourier-expansions and expansions into Gegenbauer-polynomials as discretisations of the dark energy equation of state function shows how the uncertainty on the inferred function scales with model complexity and how functional assumptions can lead to errors in extrapolation to poorly constrained redshift ranges.