頁籤選單縮合
| 題 名 | Conjugate Priors for Generalized Linear Models |
|---|---|
| 作 者 | Chen,Ming-hui; Ibrahim,Joseph G.; | 書刊名 | Statistica Sinica |
| 卷 期 | 13:2 2003.04[民92.04] |
| 頁 次 | 頁461-476 |
| 分類號 | 319 |
| 關鍵詞 | Conjugate prior; Generalized linear models; Gibbs sampling; Historical date; Logistic regression; Poisson regression; Predictive elicitation; |
| 語 文 | 英文(English) |
| 英文摘要 | 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 existence of moments of the priors under various settings, examine asymptotic properties 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. Then (y₀, a₀), along with the covariate matrix X of the current study, are used to specify the conjugate prior for the regression coefficients ß in a generalized linear model. We examine properties of the prior for a₀ fixed and for a₀ random, and study elicitation strategies for (y₀, a₀) 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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