pervariable

Pervariable is a term used in some statistical and computational modeling frameworks to denote parameters or effects that are defined for each variable in a dataset, rather than being constant across observations or groups. The term is not part of a formal standard, but it appears in discussions of variable-specific priors, hierarchical models, and feature-wise regularization. In this sense, pervariable components allow models to treat different features with distinct levels of influence or uncertainty.

In modeling terms, a pervariable approach assigns an index to coefficients or effects so that each variable can have its own parameter. For example, in a regression setting, a pervariable coefficient beta_j would index the effect of variable j. A pervariable prior might specify that beta_j comes from a distribution with hyperparameters that can vary across variables, such as beta_j ~ Normal(mu_j, sigma_j^2) with mu_j and sigma_j themselves drawn from higher-level priors. This structure can capture heterogeneity among features while still enabling sharing of information through the hierarchical framework.

Applications of pervariable concepts are common in high-dimensional data analysis, where allowing variable-specific regularization or priors helps accommodate varying signal strengths and noise levels across features. They are also used in generalized linear models and Bayesian regression to model feature-wise differences more flexibly. In data preprocessing, the adjacent concept of per-variable normalization scales each feature independently, reinforcing that the term can appear in different yet related contexts.

See also: variable-specific effects, hierarchical modeling, personalized priors, regularization, Bayesian regression.