English

On the validity of using the delta method for calculating the uncertainty of the predictions from an overparameterized model

Systems and Control 2024-10-28 v1 Systems and Control

Abstract

The uncertainty in the prediction calculated using the delta method for an overparameterized (parametric) black-box model is shown to be larger or equal to the uncertainty in the prediction of a canonical (minimal) model. Equality holds if the additional parameters of the overparameterized model do not add flexibility to the model. As a conclusion, for an overparameterized black-box model, the calculated uncertainty in the prediction by the delta method is not underestimated. The results are shown analytically and are validated in a simulation experiment where the relationship between the normalized traction force and the wheel slip of a car is modelled using e.g., a neural network

Keywords

Cite

@article{arxiv.2307.01031,
  title  = {On the validity of using the delta method for calculating the uncertainty of the predictions from an overparameterized model},
  author = {Magnus Malmström and Isaac Skog and Daniel Axehill and Fredrik Gustafsson},
  journal= {arXiv preprint arXiv:2307.01031},
  year   = {2024}
}

Comments

6 pages, 3 figures. Submitted for possible publication