We propose a novel class of conjugate priors for the family of generalized linear models. Properties of the priors are investigated in detail and elicitation issues are examined. We establish theorems characterizing the propriety and exis- tence of moments of the priors under various settings, examine asymptotic proper- ties of the priors, and investigate the relationship to normal priors. Our approach is based on the notion of specifying a prior prediction y0 for the response vector of the current study, and a scalar precision parameter a0 which quantifies one's prior belief in y0 .T hen (y0 ,a 0), along with the covariate matrix X of the current study, are used to specify the conjugate prior for the regression coefficients β in a generalized linear model. We examine properties of the prior for a0 fixed and for a0 random, and study elicitation strategies for (y0 ,a 0) in detail. We also study generalized linear models with an unknown dispersion parameter. An example is given to demonstrate the properties of the prior and the resulting posterior.
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