## Abstract

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 language | English (US) |
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Pages (from-to) | 713-724 |

Number of pages | 12 |

Journal | Statistica Sinica |

Volume | 9 |

Issue number | 3 |

State | Published - Jul 1 1999 |

## Keywords

- Conditional likelihood
- Integrated likelihood
- Marginal likelihood
- Profile likelihood

## ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty