Parametric versus non-parametric modelling? Statistical evidence based on P-value curves

Abstract

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.

Increasing adoption rates at animal shelters: a two-phase approach to predict length of stay and optimal shelter allocation

“…The author suggests this superiority comes from the lack of assumptions made about the distribution of parameter values in a dataset. Bissantz et al [ 17 ] discussed a resampling algorithm that evaluates the deviations between parametric and non-parametric methods to be noise or systematic by comparing parametric models to a non-parametric “supermodel”. Results demonstrate the non-parametric model to be significantly better.…”

Métodos estadísticos paramétricos y no paramétricos para predecir variables de rodal basados en Landsat ETM+: una comparación en un bosque de Araucaria araucana en Chile

“…Uno de los problemas del k-ésimo vecino más cercano y vecino más similar es respecto del uso de los métodos en otras áreas que las usadas para ajustar los métodos. Mayores detalles sobre estadística paramétrica y no paramétrica se pueden revisar en diversos trabajos (Potvin y Roff 1993, Baíllo y Cuevas 2003, Bissantz et al 2003, Vickers 2005, Weinand 2007), pero usualmente en ecología se tiene a inclinarse por las ventajas de los métodos no paramétri-cos (véanse las revisiones de Johnson 1995, Smith 1995, Stewart-Oaten 1995. El modelo lineal de efectos mixtos con efectos aleatorios conocidos (LME1) es la mejor opción para los datos empleados en el presente estudio (rodal 1), sin embargo, no puede ser utilizado para un área de estudio diferente donde no existen datos disponibles.…”

A review on multi-physics numerical modelling in different applications of magnetorheological fluids

“…Generally, methods of parametric modelling assume a finite set of system parameters which are all independent of any observed data, whereas non-parametric models use a set of observed data to predict future parameters of the model (Bissantz et al, 2003). Parametric and non-parametric modelling is frequently reported within MR fluid research as a classification of dynamic models developed for MR dampers.…”