Nuisance Parameter - Practical Statistics

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 tests. These provide both significance tests and confidence intervals 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 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 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.