Nuisance parameter

In statistics, a nuisance parameter is a parameter which is not of immediate interest, which nonetheless must be accounted in the analysis of some other parameters. The classic example of a nuisance parameter is the variance σ² of a normal distribution, when the mean μ is of primary interest.

In some cases, it is possible to formulate methods that circumvent nuisance parameters. The t-test is especially useful because the test statistic does not depend on the unknown variance. However, in other cases no such circumvention is known. For example, in an errors-in-variables model, the unknown true location of each observation is a nuisance parameter.

It is claimed that Bayesian inference provides a consistent, principled manner of handling nuisance parameters: every parameter aside from the parameter of interest should be integrated. As a practical matter, carrying out the required integration may be difficult and time-consuming. On a theoretical level, Bayesian methods are far from universally accepted.

Nuisance parameters are typically variances, but not always, as in the errors-in-variables example. Any parameter which intrudes on the analysis of another may be considered a nuisance parameter. Also, a parameter may cease to be a "nuisance" if it becomes the object of study, as the variance of a distribution may be.

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