 Nuisance variable

In the theory of stochastic processes in probability theory and statistics, a nuisance variable is a random variable which is fundamental to the probabilistic model, but which is of no particular interest in itself or which 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 which 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.^{[citation needed]}^{[1]}
The related term nuisance factor has been used^{[2]} 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.^{[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. 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 which 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^{[citation needed]} to nuisance parameter, given that Bayesian statistics allows parameters to be treated as having probability distributions. However this is usually avoided^{[citation needed]} as the term nuisance parameter has a specific meaning in statistical theory.
References
 ^ Eddy, S.R. (2007) "A probabilistic model of local sequence alignment that simplifies statistical significance estimation" (preprint)ftp://selab.janelia.org/pub/publications/Eddy08/Eddy08preprint.pdf
 ^ Kendall, M.G., Stuart, A. (1968) The Advanced Theory of Statistics, Volume 3: Design and Analysis, and TimeSeries, Griffin. Section 38.14, ISBN 0852640692
 ^ Irving B. Weiner, Donald K. Freedheim, John A. Schinka (2003) Handbook of Psychology, Wiley. (Chapter 1) ISBN 0471385131
 ^ Robbert Sanderman, Jim C. Coyne, Adelita V. Ranchor (2006) "Age: Nuisance variable to be eliminated with statistical control or important concern?", Patient Education and Counseling, 61 (3), 315–316. ISSN 07383991, doi:10.1016/j.pec.2006.04.002 [1]
Categories: Stochastic processes
 Latent variable models
 Statistical terminology
Wikimedia Foundation. 2010.
Look at other dictionaries:
Nuisance parameter — In statistics, a nuisance parameter is any parameter which is not of immediate interest but which must be accounted for in the analysis of those parameters which are of interest. The classic example of a nuisance parameter is the variance, σ2, of … Wikipedia
Randomized block design — In the statistical theory of the design of experiments, blocking is the arranging of experimental units in groups (blocks) that are similar to one another. Typically, a blocking factor is a source of variability that is not of primary interest to … Wikipedia
List of statistics topics — Please add any Wikipedia articles related to statistics that are not already on this list.The Related changes link in the margin of this page (below search) leads to a list of the most recent changes to the articles listed below. To see the most… … Wikipedia
Design of experiments — In general usage, design of experiments (DOE) or experimental design is the design of any information gathering exercises where variation is present, whether under the full control of the experimenter or not. However, in statistics, these terms… … Wikipedia
Optimal design — This article is about the topic in the design of experiments. For the topic in optimal control theory, see shape optimization. Gustav Elfving developed the optimal design of experiments, and so minimized surveyors need for theodolite measurements … Wikipedia
Completely randomized design — In the design of experiments, completely randomized designs are for studying the effects of one primary factor without the need to take other nuisance variables into account. This article describes completely randomized designs that have one… … Wikipedia
Analysis of variance — In statistics, analysis of variance (ANOVA) is a collection of statistical models, and their associated procedures, in which the observed variance in a particular variable is partitioned into components attributable to different sources of… … Wikipedia
Covariate — In statistics, a covariate is a variable that is possibly predictive of the outcome under study. A covariate may be of direct interest or it may be a confounding or interacting variable. The alternative terms explanatory variable, independent… … Wikipedia
Latin hypercube sampling — (LHS) is a statistical method for generating a distribution of plausible collections of parameter values from a multidimensional distribution. The sampling method is often applied in uncertainty analysis. The technique was first described by… … Wikipedia
Effect size — In statistics, an effect size is a measure of the strength of the relationship between two variables in a statistical population, or a sample based estimate of that quantity. An effect size calculated from data is a descriptive statistic that… … Wikipedia