[R-sig-ME] How to estimate assess significance of variance components

[chantepie at mnhn.fr]

Dear all,

My question could appear trivial but I still have do not still have  
found a clear answer.

BasicallyFrom what I gathered, the Bayesian framework gives us two  
possible tools to estimate significance of variances, the DIC and  
Confidence Interval (CI) estimates

DIC allows to compare models and test for significance of variances.  
XXX Some papers mention that this approach is valid for all the  
exponential family distribution models, to the extent that it should  
even allow to test which distribution fits better the data. However,  
in a previous post Jarrod mentioned that DIC does not always answer  
the hypothesis we want to test and finished by saying that for non  
gaussian distribution, he?d never use DIC. And actually, The problem  
here is that when running some animal models with Poisson distribution  
I encountered strange results suggesting ,that DIC does not work at  
all. The lower CI of Va estimates are clearly greater than 0 which let  
me think that Va is different from 0 but DIC does not give substantial  
support for models with Va
On my view,I understand that assessing confidence interval is the  
great advantage of Bayesian models. But   as Variance variances range  
between [0:1], it is not possible to construct a Pvalue by counting  
the proportion of estimate below 0 (as we could do on with covariances  
ranged between [-1:1]). When the lower CI of a variance are is far  
from 0, it is quite easy to be sure that this variance is different  
from 0 but when the posterior modes are small and lower CI are close  
to 0, how we could can we decide? One approach could be to check  
whether the posterior mode is ncelywell defined or whether it  
?collapses? on zero but would that be enough?

So I am aware that Bayesian statistics are not frequentist statistics  
and statistical tools are different but in the context of scientist  
publication (reviewers who not always know Bayesian frameworknot  
appreciating no p values), a clear decision rule would be  
neededhelpful.  the possibility of having clear decision rules appear  
almost necessary.

It would be most helpful to know your thoughts about this and May  
someone have already thought about this issue and the decision rules  
they choosewhether there are other decision rules that could be  
applied..

Thanks to all