# ⓘ Nuisance variable. In the theory of stochastic processes in probability theory and statistics, a nuisance variable is a random variable that is fundamental to t ..

## ⓘ Nuisance variable

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 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 block-means, 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.

• They are less sensitive to fault conditions, and therefore have fewer nuisance trips. This does not mean they always do, as practical performance depends
• allow for the careful conduct of designed experiments. To control for nuisance variables researchers institute control checks as additional measures. Investigators
• regression, is a method in regression analysis in which the independent variable is partitioned into intervals and a separate line segment is fit to each
• explores the relationships between several explanatory variables and one or more response variables The method was introduced by George E. P. Box and K
• integrated likelihood, is a likelihood function in which some parameter variables have been marginalized. In the context of Bayesian statistics, it may
• Non - indigenous Aquatic Nuisance Prevention and Control Act of 1990 NANPCA Organisms targeted by NISA are categorized as aquatic nuisance species, including
• estimated parameter as a random variable whereas frequentist confidence intervals treat their bounds as random variables and the parameter as a fixed value
• line, anglers do not consider it a desirable catch, and often find it a nuisance while going after trout. Wildlife agencies have even tried eradication
• Datanami. February 1, 2016. Retrieved February 1, 2016. How a Nuisance Variable Turned Into Potential Lifesaver Datanami. January 4, 2016. Retrieved
• handle the nuisance parameter s of the common success probability when calculating the p - value. Fisher s test avoids estimating the nuisance parameter s
• certain conditions must be met. Nuisance parameters should be known, or estimated with high accuracy an example of a nuisance parameter would be the standard

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