Reweights

Reweights, in statistical and data analysis contexts, refer to the set of weights assigned to observations, samples, or events to adjust their influence in calculations. Weights are positive numbers that scale contributions to estimators, expectations, or losses, allowing analysts to reflect a target distribution or correct biases in the data.

In survey research and population studies, reweighting is used to align sample characteristics with known population margins. Techniques such as post-stratification and raking adjust weights so that weighted sample distributions agree with external benchmarks. In machine learning and data science, sample weighting is employed to address class imbalance, varying misclassification costs, or differing data quality by incorporating weights into loss functions or evaluation metrics.

In Monte Carlo methods and physics analyses, reweighting modifies the contribution of simulated events when changing model parameters, detector effects, or theoretical assumptions. If samples are drawn from a distribution p(x) but the analysis targets q(x), each sample is assigned a weight w(x) = q(x)/p(x). This principle underpins importance sampling, enabling estimation of expectations under q using p-samples.

Common reweighting methods include importance sampling (likelihood-ratio weights), inverse probability weighting (used in causal inference), propensity score weighting, and calibration or post-stratification weights. Kernel-based reweighting and other smoothing approaches can address continuous covariates or complex target distributions. Careful design aims to keep weights stable and avoid excessive variance.

Limitations include increased estimator variance from highly variable weights and reduced effective sample size. Diagnostics such as weight distribution checks, overlap assessment between source and target distributions, and sensitivity analyses are important to ensure reliable results. See also: importance sampling, propensity scores, post-stratification, raking.