downweight

Downweight is a data analysis practice in which certain observations or variables are assigned smaller weights in a calculation, reducing their influence on the resulting estimates. It is used to reflect uncertainty, data quality, or relevance, and can also arise from algorithms designed to limit the impact of problematic data. Downweighting contrasts with equal weighting or upweighting of data points.

In regression and estimation, downweighting is commonly implemented through weights. In weighted least squares, each observation i is given a weight w_i that scales its contribution to the objective function; observations with higher variance, measurement error, or lower reliability receive smaller weights. Robust regression methods also downweight outliers, using weight functions such as the Huber or Tukey biweight to diminish the influence of large residuals.

In Bayesian analysis, downweighting can be achieved by tempering the likelihood or using power priors. This reduces the influence of individual observations on the posterior distribution, effectively reflecting uncertainty about the data-generating process. In meta-analysis, studies are often downweighted by inverse variance or quality scores to reflect precision and credibility.

Other contexts include time-series models with forgetting factors that give less weight to older observations, and feature or model weighting where less relevant components are de-emphasized. Considerations when downweighting include the choice of weighting scheme, potential bias, and the trade-off between robustness and efficiency.