A New Perspective on Priors for Generalized Linear Models
作者:
EdwardJ. Bedrick,
Ronald Christensen,
Wesley Johnson,
期刊:
Journal of the American Statistical Association
(Taylor Available online 1996)
卷期:
Volume 91,
issue 436
页码: 1450-1460
ISSN:0162-1459
年代: 1996
DOI:10.1080/01621459.1996.10476713
出版商: Taylor & Francis Group
关键词: Conditional means priors;Data augmentation priors;Exponential regression;Gamma regression;Linear models;Log-linear models;Logistic regression;Poisson regression
数据来源: Taylor
摘要:
This article deals with specifications of informative prior distributions for generalized linear models. Our emphasis is on specifying distributions for selected points on the regression surface; the prior distribution on regression coefficients is induced from this specification. We believe that it is inherently easier to think about conditional means of observables given the regression variables than it is to think about model-dependent regression coefficients. Previous use of conditional means priors seems to be restricted to logistic regression with one predictor variable and to normal theory regression. We expand on the idea of conditional means priors and extend these to arbitrary generalized linear models. We also consider data augmentation priors where the prior is of the same form as the likelihood. We show that data augmentation priors are special cases of conditional means priors. With current Monte Carlo methodology, such as importance sampling and Gibbs sampling, our priors result in tractable posteriors.
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