[R-sig-ME] How to usepriors in MCMCglmm?

Jarrod Hadfield j.hadfield at ed.ac.uk
Sat Jan 29 15:56:05 CET 2011


Sorry for the long delay - too much work!

I'm reluctant to give general recommendations for priors because  
appropriate priors will vary with the model, the (transformed)  
parameters of interest and the intended properties of the prior  
(informative or weakly informative).

 From the questions I get asked, I think most people are concerned  
with having weakly informative priors on (co)variances, or functions  
of (co)variances such as correlations or repeatabilities/heritabilities.

The posterior mode under some improper priors coincide with the REML  
point estimates, and for this reason they are sometimes used. In  
Section 1.5 of the Course Notes I have listed improper priors that  
result in posterior modes equal to the REML estimate.  One that I did  
not discuss is a model with two variances and inference focuses on the  
proportion of variance explained by each (e.g. r2 = Va/(Va+Ve)) where  
Va and Ve are tow variances. A prior for both with V=0 and nu=2  
results in a prior for r2 that is flat on the interval 0 to 1.

Improper priors can cause problems: the posterior may not be proper,  
mixing may be an issue, and numerical errors may happen causing  
MCMCglmm to terminate. Also, although he point estimates may agree  
with frequentists approaches it does not mean that the posterior as  
whole has desirable properties.

In MCMCglmm the most flexible prior specification for variances can be  
achieved using parameter expanded priors (scaled non-central F ),  
which includes the inverse-Wishart as a special case.  The prior V=1,  
nu=0.002 used to be used regularly (and perhaps still is?) in WinBUGS  
and is the same as an inverse-gamma with shape=scale=0.001.  It has  
some unfortunate properties when the data give support to values of  
the variance close to zero. You should read: Gelman A (2006). Bayesian  
Analysis, 1(3), 515–533. I think the suggestion  V=some_variance,nu=1  
from Wilson's ecologists guide (and the old MCMCglmm tutorial which  
I've scrapped) will be quite informative in many instances, and I  
would not recommend it as a general weakly-informative prior.

Parameter expanded priors (again see Gelman & Chapter 9 of the  
CourseNotes) seem to have better properties and also mix better, but I  
do not think their properties have been well worked out for the multi  
parameter case (e.g. their influence on  
covariances/correlations/heritabilities). This may be my ignorance,  
and I would be happy if someone could point me to the relevant  
literature if it exists.



Quoting Szymek Drobniak <geralttee at gmail.com>:

> Hi all,
> I'm trying to make some information about using MCMCglmm more systematic,
> but the picture I'm getting from this list and resources on MCMCglmm is a
> little blurry. Could you at least try ;) provide simple criteria that could
> be used to tell whne to use proper and when (we could possibly) use improper
> priors? In general I've been using proper priors and I don;t have much
> experience with improper ones.Also - based on your own experience which
> prior specifications you find more useful? E.g.
> list(R=list(V=1,nu=0.002),G=list(G1=list(V=1,nu=0.002))) is commonly used
> but Wilson's ecologists guide to theanimal model suggests using priors like
> this:
> list(R=list(V=some_variance,nu=1),G=list(G1=list(V=some_variance,nu=1))) (of
> course for gaussian data, single variances).
> Any help will be appreciated!
> Cheers,
> sz.
> --
> Szymon Drobniak || Population Ecology Group
> *Institute of Environmental Sciences, Jagiellonian University
> ul. Gronostajowa 7, 30-387 Kraków, POLAND
> *tel.: +48 12 664 52 19 fax: +48 12 664 69 12
> www.eko.uj.edu.pl/drobniak
> 	[[alternative HTML version deleted]]

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