Deviance information criterion for Bayesian model selection: Justification and variation
Deviance information criterion (DIC) has been extensively used for making Bayesian model selection. It is a Bayesian version of AIC and chooses a model that gives the smallest expected Kullback-Leibler divergence between the data generating process (DGP) and a predictive distribution asymptotically....
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| Main Authors: | , , |
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| Format: | text |
| Language: | English |
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Institutional Knowledge at Singapore Management University
2017
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| Subjects: | |
| Online Access: | https://ink.library.smu.edu.sg/soe_research/1927 https://ink.library.smu.edu.sg/context/soe_research/article/2926/viewcontent/DICTheory10.pdf |
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| Institution: | Singapore Management University |
| Language: | English |
| Summary: | Deviance information criterion (DIC) has been extensively used for making Bayesian model selection. It is a Bayesian version of AIC and chooses a model that gives the smallest expected Kullback-Leibler divergence between the data generating process (DGP) and a predictive distribution asymptotically. We show that when the plug-in predictive distribution is used, DIC can have a rigorous decision-theoretic justification under regularity conditions. An alternative expression for DIC, based on the Bayesian predictive distribution, is proposed. The new DIC has a smaller penalty term than the original DIC and is very easy to compute from the MCMC output. It is invariant to reparameterization and yields a smaller expected loss than the original DIC asymptotically. |
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