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Identifiability, improper priors, and Gibbs sampling for generalized linear models

Identifiability, improper priors, and Gibbs sampling for generalized linear models
Identifiability, improper priors, and Gibbs sampling for generalized linear models
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.
0162-1459
247-253
Gelfand, Alan E.
1dc59cf1-5e5f-4001-b1f9-92b0a8e2f64f
Sahu, Sujit K.
33f1386d-6d73-4b60-a796-d626721f72bf
Gelfand, Alan E.
1dc59cf1-5e5f-4001-b1f9-92b0a8e2f64f
Sahu, Sujit K.
33f1386d-6d73-4b60-a796-d626721f72bf

Gelfand, Alan E. and Sahu, Sujit K. (1999) Identifiability, improper priors, and Gibbs sampling for generalized linear models. Journal of the American Statistical Association, 94 (445), 247-253.

Record type: Article

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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Published date: 1999
Organisations: Statistics

Identifiers

Local EPrints ID: 30030
URI: http://eprints.soton.ac.uk/id/eprint/30030
ISSN: 0162-1459
PURE UUID: 35afbb85-f784-48b0-84fc-0b1a28695e55
ORCID for Sujit K. Sahu: ORCID iD orcid.org/0000-0003-2315-3598

Catalogue record

Date deposited: 19 Mar 2007
Last modified: 17 Dec 2019 01:52

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