A graphical selection method for parametric models in noisy inhomogeneous regression

A common problem in physics is to fit regression data by a parametric class of functions, and to decide whether a certain functional form allows for a good fit to the data. Common goodness‐of‐fit methods are based on the calculation of the distribution of certain statistical quantities under the assumption that the model under consideration holds true . This process has methodological flaws, e.g. a good ‘fit’– albeit with a model that is wrong – might be caused by overfitting or the fact that the chosen statistical criterion is not powerful enough to distinguish the particular deviation between the model and the true regression function. This causes particular difficulties when models with different numbers of parameters are to be compared. Therefore, the number of parameters is often also penalized. We provide a methodology that circumvents these problems to some extent. It is based on the consideration of the error distribution of the goodness‐of‐fit criterion under a broad range of possible models – and not only under the assumption that a given model holds true. We present a graphical method to decide on the most evident model from a range of parametric models of the data. The method allows one to quantify statistical evidence for the model (up to some distance between the model and the true regression function) and not only absence of evidence against, as common goodness‐of‐fit methods do. Finally, we apply our method to the problem of recovering the luminosity density of the Milky Way from a dereddened COBE /DIRBE L ‐band map. We present statistical evidence for flaring of the stellar disc inside the solar circle.