Summary: The problem of eliminating nuisance parameters is tackled from different points of view. Standard likelihood techniques, such as profile likelihood and its modifications, are compared with a Bayesian analysis based on reference priors. Examples are considered to illustrate what happens in multiparameter problems.
In particular the frequentist coverage probabilities of the credible sets derived from the reference priors are shown to be better than those computed from a likelihood approach. Advantages and disadvantages of Bayesian and likelihood analyses are discussed.