Data Fitting and Uncertainty: A practical introduction to weighted least squares and beyond

By T. Strutz. 2010

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A Hybrid Prognostics Approach for Estimating Remaining Useful Life of Rolling Element Bearings (2020, methodology): “In this paper, the nonlinear least square [33] is employed to estimate these unknown parameters.”
Human perturbations reduce dung beetle diversity and dung removal ecosystem function (2021, methodology): “In the presence of heteroscedasticity in the residuals of several models, we applied weighted least square regression (Strutz, 2016) by including weights (1/variance) into the model using the extract model weights function.”
A high-resolution canopy height model of the Earth (2022, background): “While inverse-variance weighting is known to yield the lowest expected error 38 , we observe a deterioration of the uncertainty calibration for low values ( 4 m standard deviation in Extended Data Fig.”
Optimism-driven exploration for nonlinear systems (2015, background): “Weighted least squares is generally considered robust and accurate but computationally expensive [22], since it normally must access the entire training set for each prediction.”
Discriminative Least Squares Regression for Multiclass Classification and Feature Selection (2012, background): “Many variants have been developed, including weighted LSR [1], partial LSR [2], and other extensions (for example, ridge regression [3]).”