On the relationship between Bayesian and non-Bayesian elimination of nuisance parameters

Thomas A. Severini*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

24 Scopus citations


Consider a statistical model parameterized by a scalar parameter of interest θ and a nuisance parameter λ. Many methods of inference are based on a "pseudo-likelihood" function, a function of the data and θ that has properties similar to those of a likelihood function. Commonly used pseudo-likelihood functions include conditional likelihood functions, marginal likelihood functions, and profile likelihood functions. From the Bayesian point of view, elimination of λ is easily achieved by integrating the likelihood function with respect to a conditional prior density π(λ|θ); this approach has some well-known optimality properties. In this paper, we study how close certain pseudo-likelihood functions are to being of Bayesian form. It is shown that many commonly used non-Bayesian methods of eliminating λ correspond to Bayesian elimination of λ to a high degree of approximation.

Original languageEnglish (US)
Pages (from-to)713-724
Number of pages12
JournalStatistica Sinica
Issue number3
StatePublished - Jul 1 1999


  • Conditional likelihood
  • Integrated likelihood
  • Marginal likelihood
  • Profile likelihood

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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