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Identifiability, Improper Priors, and Gibbs Sampling for Generalized Linear Models

Alan E. Gelfand and Sujit K. Sahu
Journal of the American Statistical Association
Vol. 94, No. 445 (Mar., 1999), pp. 247-253
DOI: 10.2307/2669699
Stable URL: http://www.jstor.org/stable/2669699
Page Count: 7
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Identifiability, Improper Priors, and Gibbs Sampling for Generalized Linear Models
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Abstract

Markov chain Monte Carlo algorithms are widely used in the fitting of generalized linear models (GLMs). Such model fitting is somewhat of an art form, requiring suitable trickery and tuning to obtain results in which one can have confidence. A wide range of practical issues arise. The focus here is on parameter identifiability and posterior propriety. In particular, we clarify that nonidentifiability arises for usual GLMs and discuss its implications for simulation-based model fitting. Because often some part of the prior specification is vague, we consider whether the resulting posterior is proper, providing rather general and easily checked results for GLMs. We also show that if a Gibbs sampler is run with an improper posterior, then it may be possible to use the output to obtain meaningful inference for certain model unknowns.

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