Randependent

Randependent is a term used in probability and statistics to describe a modeling concept that blends randomization with dependence structures in a multivariate system. In common usage, randependent describes a scenario where the joint distribution of a set of random variables exhibits both independent and dependent relationships mediated by shared random factors. The term is not part of a formal, canonical vocabulary; definitions vary by author, but the core idea is to capture situations where components behave independently most of the time, yet occasionally experience dependence due to a common latent source.

Definition and interpretation: A typical randependent model posits a latent random variable Z that induces dependency among observed variables X1, ..., Xn. Conditional on Z, the Xi may be independent, but unconditional independence does not hold; thus, the variables are randependent via Z. Alternatively, randependence may describe time-varying dependence: components are independent within regimes but dependent across regimes determined by random regime switches.

Relation to existing concepts: Randependent overlaps with conditional independence, latent-variable models, and regime-switching models. It is distinct from mutual independence, which requires independence without conditioning.

Applications: The concept appears in simulation, risk modeling, and econometrics to reproduce systems where shocks create shared outcomes while individual factors drive outcomes in isolation under other conditions.

See also: independence, conditional independence, latent variable models, regime-switching, stochastic processes.

References: Because randependent is a coined or informal term, standard formal definitions vary; readers are directed to discussions of conditional independence and latent variable modeling for formal foundations.