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Posterior mode estimation for the generalized linear model. (English) Zbl 0781.62111

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

Software:

GLIM
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