Eaves, D. M.; Chang, T. Posterior mode estimation for the generalized linear model. (English) Zbl 0781.62111 Ann. Inst. Stat. Math. 44, No. 3, 417-434 (1992). Summary: Posterior mode estimators are poposed, which arise from simply expressed prior opinion about expected outcomes, roughly as follows: a conjugate family of prior distributions is determined by a given variance function. Using a conjugate prior, a posterior mode estimator and its estimated (co)-variances are obtained through conventional maximum likelihood computations, by means of small alterations to the observed outcomes and/or to the modelled variance function. Within the conjugate family, for purposes of inference about the regression vector, a reference prior is proposed for a given choice of linear design of the canonical link. The resulting approximate reference inferences approximate the Bayesian inferences which arise from a “minimally informative” reference prior. A set of subjective prior upper and lower percentage points for the expected outcomes can be used to determine a conjugate family member. Alternatively, a set of subjective prior means and standard deviations determine a member. The subfamily of priors determinable by percentage points either includes or approximates the proposed reference prior. MSC: 62J12 Generalized linear models (logistic models) 62F15 Bayesian inference Keywords:contingency tables; exponential family; frequency counts; Jeffreys prior; logistic regression; multinomial outcome; minimally informative prior; quasi-likelihood; conjugate family of prior distributions; given variance function; posterior mode estimator; maximum likelihood; reference prior; linear design of the canonical link; subjective prior means; standard deviations; percentage points Software:GLIM PDFBibTeX XMLCite \textit{D. M. Eaves} and \textit{T. Chang}, Ann. Inst. Stat. Math. 44, No. 3, 417--434 (1992; Zbl 0781.62111)