An invitation to coupling and copulas: with applications to multisensory modeling

TL;DR

This paper introduces the concepts of coupling and copulas in stochastic modeling, illustrating their applications in multisensory perception and providing pointers to advanced treatments.

Contribution

It offers an accessible introduction to coupling and copulas, highlighting their roles in multisensory modeling and linking to recent developments in the field.

Findings

Coupling allows constructing joint distributions without a shared probability space.

Copulas connect multivariate distributions to their marginals.

Applications demonstrated in multisensory perception modeling.

Abstract

This paper presents an introduction to the stochastic concepts of \emph{coupling} and \emph{copula}. Coupling means the construction of a joint distribution of two or more random variables that need not be defined on one and the same probability space, whereas a copula is a function that joins a multivariate distribution to its one-dimensional margins. Their role in stochastic modeling is illustrated by examples from multisensory perception. Pointers to more advanced and recent treatments are provided.