The weighted likelihood

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Weighted likelihood copula modeling of extreme rainfall events in Connecticut. (2010, methodology): “We approach the122 problem by pooling observations from stations nearby to construct the weighted likelihood123 (Hu and Zidek, 2002).”
The Real-World-Weight Cross-Entropy Loss Function: Modeling the Costs of Mislabeling (2020, background): “Weighted maximum likelihood estimators [14] address the challenges of imbalanced classes from the perspective of Maximum Likelihood Estimation [15].”
Fermi Large Area Telescope Fourth Source Catalog (2019, methodology): “This can be adapted to the maximum likelihood framework by introducing weights wi 1 (Hu & Zidek 2002) as ( ) ( )å= - w n M Mlog log 12 i i i i i where Mi and ni are the model and observed counts in each bin, and the sum runs over all bins in space and energy.”
Confidence Distributions and a Unifying Framework for Meta-Analysis (2011, methodology): “…here are fixed and nonadaptive weights, although under some mild restrictions the development can be extended to include adaptive weights including those used in Section 4.1 or something similar to those used in Hu and Zidek (2002) or Wang and Zidek (2005) in the context of weighted likelihood.”