Weighting

Weighting refers to the assignment of weights to elements in a set, where a weight is a nonnegative value that reflects relative importance, frequency, probability, or reliability. When combined, weights influence aggregates or decisions more than others.

In statistics, weights are used to compute weighted averages, variances, and regression models. The weighted mean is the sum of each value times its weight divided by the sum of weights. Weights may reflect sample size, measurement precision, or sampling design. In survey sampling, weights adjust for unequal selection probabilities and nonresponse; calibration and raking adjust weights to known population totals. In inverse-probability weighting, observations with lower probability of selection receive higher weights to correct bias.

In estimation and optimization, weighted least squares minimizes a weighted sum of squared residuals, giving more influence to observations with smaller variance or higher reliability. In machine learning and data science, features or classes can be weighted, and loss functions can include class weights to address imbalanced data.

In information retrieval and text analysis, weighting schemes such as TF-IDF assign weights to terms based on frequency in a document and rarity across the corpus, improving ranking. Weighting also appears in signal processing and data fusion with window functions or measurement weighting.

In decision analysis, weights express the relative importance of criteria in multi-criteria decision analysis, allowing a composite score to reflect stakeholder priorities.