演講公告 91年1月3日 (星期四)

摘要

We propose a class of conjugate priors for the family of generalized linear models. Properties of the prior are investigated in detail and elicitation issues are examined. We establish theorems characterizing the propriety and existence of moments of the prior under various settings, examine asymptotic properties of the prior, and investigate its relationship to the normal prior. Specifically, our proposed 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. Then, (y0,a0), along with the covariate matrix X of the current study, are used to specify the conjugate prior for the regression coefficients b in a generalized linear model. The motivation behind this approach is that it is often easier to think about, and directly interpret observable quantities when specifying a prior, since the investigator often has prior information on the observables from training data, historical data, summary statistics, a theoretical prediction model, or from expert opinion and case-specific information on the subjects in the current study. This information is often quantifiable in the form of a vector of prior predictions for the response vector of the current study, thus making elicitation easier than a direct specification of a prior mean and covariance matrix for b. We examine properties of the prior for a0 fixed and for a0 random, and study elcitation strategiesfor (y0, a0) in detail. We also study generalized linear models with an unknown dispersion parameter. Examples are given to demonstrate the properties of the prior and the resulting posterior.