In the theory of stochastic processes in probability theory and statistics, a nuisance variable is a random variable that is fundamental to the probabilistic model, but that is of no particular interest in itself or is no longer of any interest: one such usage arises for the Chapman–Kolmogorov equation.
For example, a model for a stochastic process may be defined conceptually using intermediate variables that are not observed in practice.
[1] The related term nuisance factor has been used[2] in the context of block experiments, where the terms in the model representing block-means, often called "factors", are of no interest.
[3] "Nuisance variable" has been used in the context of statistical surveys to refer information that is not of direct interest but which needs to be taken into account in an analysis.
[4] In the context of stochastic models, the treatment of nuisance variables does not necessarily involve working with the full joint distribution of all the random variables involved, although this is one approach.