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Bayesian Deviance, the Effective Number of Parameters, and the Comparison of Arbitrarily Complex Models
, 1998
"... We consider the problem of comparing complex hierarchical models in which the number of parameters is not clearly defined. We follow Dempster in examining the posterior distribution of the loglikelihood under each model, from which we derive measures of fit and complexity (the effective number of p ..."
Abstract

Cited by 28 (7 self)
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We consider the problem of comparing complex hierarchical models in which the number of parameters is not clearly defined. We follow Dempster in examining the posterior distribution of the loglikelihood under each model, from which we derive measures of fit and complexity (the effective number of parameters). These may be combined into a Deviance Information Criterion (DIC), which is shown to have an approximate decisiontheoretic justification. Analytic and asymptotic identities reveal the measure of complexity to be a generalisation of a wide range of previous suggestions, with particular reference to the neural network literature. The contributions of individual observations to fit and complexity can give rise to a diagnostic plot of deviance residuals against leverages. The procedure is illustrated in a number of examples, and throughout it is emphasised that the required quantities are trivial to compute in a Markov chain Monte Carlo analysis, and require no analytic work for new...
Examples Volume 1 (version
"... Introduction and Disclaimer These worked examples illustrate the use of the BUGS language and sampler in a wide range of problems. They contain a number of useful "tricks", but are certainly not exhaustive of the models that may be analysed. We emphasise that all the results for these examples have ..."
Abstract
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Introduction and Disclaimer These worked examples illustrate the use of the BUGS language and sampler in a wide range of problems. They contain a number of useful "tricks", but are certainly not exhaustive of the models that may be analysed. We emphasise that all the results for these examples have been derived in the most naive way: in general a burnin of 500 iterations and a single long run of 1000 iterations. This is not recommended as a general technique: no tests of convergence have been carried out, and traces of the estimates have not even been plotted. However, comparisons with published results have been made where possible. Times have been measured on a 60 MHz superSPARC: a 60 MHz Pentium PC appears to be about 4 times slower, and a 30 MHz superSPARC about 2 times slower. Users are warned to be extremely careful about assuming convergence, especially when using complex models including errors in variables, crossed random effects and intrinsi