Prior Distributions From Pseudo-Likelihoods in the Presence of Nuisance Parameters

• 成果类型: Article
• 署名作者: Ventura, Laura; Cabras, Stefano; Racugno, Walter
• 署名单位: University of Padua; University of Cagliari
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/jasa.2009.0133
• 发表日期: 2009
• 页码: 768-774
• 关键词: probability matching priors; bayesian-inference; Empirical Likelihood; frequentist validity; elimination; intervals; PROPERTY

摘要

Consider a mode parameterized by 0 = (psi, lambda), where psi is the parameter of interest. The problern of eliminating the nuisance parameter lambda the nuis can be tackled by resorting to a pseudo-likelihood function L*(psi) for psi-namely a function of psi only and the data y with properties similar to those of a likelihood function. If one treats L*(psi) as a true likelihood. the posterior distribution pi*(psi vertical bar y) alpha pi(psi)L*(psi) for psi can be considered. where pi(psi) is a prior distribution on psi. The goal of this article is to construct probability matching priors for a scalar parameter of interest only (i.e., priors for which Bayesian and frequentist inference agree to some order of approximation) to be used in pi*(psi vertical bar y). When L*(psi) is it margpinal, a conditional, or a modification of the profile likelihood. we show that pi(psi) is simply proportional to the square root of the inverse of the asymptotic variance of the pseudo-maxinium likelihood estimator. The proposed priors are compared with the reference or Jeffreys' priors in four examples.