Hi,

thanks for your answer! In the end I just went through all possibilities and
got a very general point of view, which is quite similar to your
suggestions. I found Van Dongen, 2006 (Journal of theoretical biology) very
useful, apart from Gelman's paper. I tried to find somothing useful on
Cauchy priors for more complex (co)variance structures but it seems it's
realy still unexplored... Thanks for your help anyway!

Cheers,
sz.

On 29 January 2011 15:56, Jarrod Hadfield <j.hadfield@ed.ac.uk> wrote:

> Hi,
>
> 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.
>
> Cheers,
>
> Jarrod
>
>
>
>
> Quoting Szymek Drobniak <geralttee@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]]
>>
>>
>>
>
>
> --
> The University of Edinburgh is a charitable body, registered in
> Scotland, with registration number SC005336.
>
>


-- 
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

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