[R-sig-ME] How to assess significance of variance components (Please discard previous e mail... but read this one)

[chantepie at mnhn.fr]

Dear all,

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

 From 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.  
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, 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
I understand that assessing confidence interval is the great advantage  
of Bayesian models. But as 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 with covariances). When the lower CI of a  
variance 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 can we decide? One approach could be to check  
whether the posterior mode is well defined or whether it ?collapses?  
on zero but would that be enough?


I am aware that Bayesian statistics are not frequentist statistics and  
statistical tools are different but, a clear decision rule would be  
helpful.

It would be most helpful to know your thoughts about this and whether  
there are other decision rules that could be applied.

Thanks to all

Stephane