VarianceBased

Variancebased is an umbrella term used to describe methods, analyses, or criteria that rely on variance as a central measure. It is not a single theory but a family of approaches found across statistics, data analysis, and related fields.

In statistics and experimental design, variance-based methods perform variance decomposition to attribute observed variability to factors, interactions, and random error. The classic example is analysis of variance (ANOVA). Modern variance-based sensitivity analysis (VBSA) uses the variance of model outputs to apportion influence among inputs, often employing Sobol indices or related techniques to quantify each input’s contribution to total output variance.

In data preprocessing and machine learning, variance-based feature selection uses feature variance as a criterion for removing low-variance features before modeling. While high-variance features can carry information, this approach requires caution because variance alone does not guarantee predictive power, and some important predictors may have low variance. Variance thresholds are a common practical tool in this context.

In quality control and reliability, variance-based measures assess dispersion and stability of processes or systems, including monitoring changes in process variance over time as an indicator of drift or instability.

Limitations of variancebased approaches include sensitivity to outliers, reliance on certain statistical assumptions, and the possibility that variance misses important distributional characteristics such as skewness or multimodality. When applied appropriately, variancebased methods provide a concise summary of dispersion and a basis for attributing variation to its sources.

See also: variance, analysis of variance, sensitivity analysis, Sobol indices, feature selection, design of experiments.