Nuisance variable
nuisance variable, nuisance variable exampleIn 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 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 If the problem is to derive the theoretical properties, such as the mean, variance and covariances of quantities that would be observed, then the intermediate variables are nuisance variables
The related term nuisance factor has been used in the context of block experiments, where the terms in the model representing blockmeans, often called "factors", are of no interest Many approaches to the analysis of such experiments, particularly where the experimental design is subject to randomization, treat these factors as random variables More recently, "nuisance variable" has been used in the same context
"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
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 Instead, an analysis may proceed directly to the quantities of interest
The term nuisance variable is sometimes also used in more general contexts, simply to designate those variables that are marginalised over when finding a marginal distribution In particular, the term may sometimes be used in the context of Bayesian analysis as an alternative to nuisance parameter, given that Bayesian statistics allows parameters to be treated as having probability distributions However this is usually avoided as the term nuisance parameter has a specific meaning in statistical theory
References
 ^ Eddy, S R 2008 Rost, Burkhard, ed "A Probabilistic Model of Local Sequence Alignment That Simplifies Statistical Significance Estimation" PLoS Computational Biology 4 5: e1000069 doi:101371/journalpcbi1000069 PMC 2396288 PMID 18516236
 ^ Kendall, MG, Stuart, A 1968 The Advanced Theory of Statistics, Volume 3: Design and Analysis, and TimeSeries, Griffin Section 3814, ISBN 0852640692
 ^ Irving B Weiner, Donald K Freedheim, John A Schinka 2003 Handbook of Psychology, Wiley Chapter 1 ISBN 0471385131
 ^ Sanderman, R; Coyne, J C; Ranchor, A V 2006 "Age: Nuisance variable to be eliminated with statistical control or important concern" Patient Education and Counseling 61 3: 315–316 doi:101016/jpec200604002 PMID 16731313
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