Editing Nuisance parameter (section)

==Practical statistics==
Practical approaches to statistical analysis treat nuisance parameters somewhat differently in frequentist and Bayesian methodologies.

A general approach in a frequentist analysis can be based on maximum [[likelihood-ratio test]]s. These provide both [[significance test]]s and [[confidence interval]]s for the parameters of interest which are approximately valid for moderate to large sample sizes and which take account of the presence of nuisance parameters. See [[Debabrata Basu|Basu]] (1977) for some general discussion and Spall and Garner (1990) for some discussion relative to the identification of parameters in linear dynamic (i.e., [[state space representation]]) models.

In [[Bayesian analysis]], a generally applicable approach creates random samples from the joint posterior distribution of all the parameters: see [[Markov chain Monte Carlo]]. Given these, the joint distribution of only the parameters of interest can be readily found by [[marginalization (probability)|marginalizing]] over the nuisance parameters. However, this approach may not always be computationally efficient if some or all of the nuisance parameters can be eliminated on a theoretical basis.