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I'm trying to figure out why certain methods are used for comparing models in Bayesian statistics. DIC is often used in Bayesian model comparison. However, I'm under the impression that one could calculate likelihood and/or BIC, too.

Specifically, I've been told that the calculation of likelihood could depend on 'how one marginalizes over parameters'. What does this mean? Are there other reasons why some people don't prefer BIC?

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In my experience, people often prefer to use the DIC only because it is a default feature of output in BUGS. However, the BIC can always be calculated although often times it can be a very hard/nasty integral to work with. Furthermore, if your prior distribution is not proper, the BIC can lead to some very unfavorable results.

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  • $\begingroup$ I was under the impression that SIAR (stable isotope analysis in R) gave the BIC. I could be wrong though. Is the BIC necessarily determined analytically? $\endgroup$
    – rbatt
    Commented Jul 10, 2013 at 17:16

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