2003/01/10 by N. Bissantz, A. Munk, A. Scholz
Computer Science · Physics and Astronomy · #Galaxies: Formation, Evolution, Phenomena #Gaussian Processes and Bayesian Inference #Statistical Mechanics and Entropy #astro-ph
paper · pdf · doi:10.1046/j.1365-8711.2003.06377.x
Accepted for publication in MNRAS
arxiv created 2003/01/10 · openalex publication_date 2003/04/21 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
In astrophysical (inverse) regression problems it is an important task to decide whether a given parametric model describes the observational data sufficiently well or whether non-parametric modelling becomes necessary. However, in contrast to common practice this cannot be decided solely by comparing the quality of fit owing to possible overfitting by the non-parametric method. Therefore, in this paper we present a resampling algorithm that allows one to decide whether deviations between a parametric and a non-parametric model are systematic or caused by noise. The algorithm is based on a statistical comparison of the corresponding residuals, under the assumption of the parametric model and under violation of this assumption. This yields a graphical tool for a robust decision making of parametric versus non-parametric modelling. Moreover, our approach can be used for the selection of the most appropriate model among several possibilities (model selection). The methods are illustrated by the problem of recovering the luminosity density in the Milky Way (MW) from near-infrared (NIR) surface brightness data of the DIRBE experiment on-board the COBE satellite. Among the parametric models investigated one with a four-armed spiral structure performs best. In this model the Sagittarius—Carina arm and its counter-arm are significantly weaker than the other pair of arms. Furthermore, we find statistical evidence for an improvement over a range of parametric models with different spiral structure morphologies using a non-parametric model by Bissantz & Gerhard.