<> "The repository administrator has not yet configured an RDF license."^^ . <> . . "Statistical Inference in Cosmology - From Parameters to Learnable Functions"^^ . "Inference tasks on non-Gaussian posterior distributions are commonly approached using Markov chain Monte Carlo. We draw an analogy to canonical partition functions defined as Laplace transforms of the Bayesian likelihood and prior. This allows to derive analytical expressions for cumulants of the posterior. At second order, we recover the conventional Fisher matrix formalism. We find a closed formula for cumulants of weakly non-Gaussian posteriors. Additionally, we use this formalism to construct physically motivated convergence criteria with clearly defined target values based on virialization, equipartition, and thermalization of the Markov chain. We successfully validate these approaches using a dark energy model applied to supernova data. To speed up forward simulation we use physics-informed neural networks (PINNs). They provide fast and accurate predictions of the luminosity distance for a given choice of parameters. Using the same architecture we perform a model-independent, parameter-free reconstruction of the Hubble function. The PINN uncertainties are quantified using a heteroscedastic loss and repulsive ensembles. Continuing in the vein of fast simulations, we construct the parallelized inflation solver PARALLIZIS, based on the Madelung transformed perturbation equations. It provides a forward simulation from arbitrary inflaton potentials to the primordial power spectrum, while allowing for GPU parallelization."^^ . "2025" . . . . . . . "Lennart Kai"^^ . "Röver"^^ . "Lennart Kai Röver"^^ . . . . . . "Statistical Inference in Cosmology - From Parameters to Learnable Functions (PDF)"^^ . . . "dissertation.pdf"^^ . . . "Statistical Inference in Cosmology - From Parameters to Learnable Functions (Other)"^^ . . . . . . "indexcodes.txt"^^ . . . "Statistical Inference in Cosmology - From Parameters to Learnable Functions (Other)"^^ . . . . . . "lightbox.jpg"^^ . . . "Statistical Inference in Cosmology - From Parameters to Learnable Functions (Other)"^^ . . . . . . "preview.jpg"^^ . . . "Statistical Inference in Cosmology - From Parameters to Learnable Functions (Other)"^^ . . . . . . "medium.jpg"^^ . . . "Statistical Inference in Cosmology - From Parameters to Learnable Functions (Other)"^^ . . . . . . "small.jpg"^^ . . "HTML Summary of #35981 \n\nStatistical Inference in Cosmology - From Parameters to Learnable Functions\n\n" . "text/html" . . . "530 Physik"@de . "530 Physics"@en . .