[R-sig-ME] various priors for MCMCglmm

[Celine Teplitsky]

Dear all,

I was just wondering if anyone had commented or would have things to add 
on the email previously sent by Ned. As a non specialist, I would also 
be very interested on reading further clarification on these issues

Thanks a lot in advance

Celine

> So in going back over some of this it is clear that my understanding of nu
> is still very much lacking, making the multivariate generalizations perhaps
> inappropriate. Part of this seems to be that nu incorporates both "degree of
> belief" and some aspects of the shape of the prior distribution, at least
> for the inverse gamma.
>
> Can anyone recommend some general texts that might clarify some of this?
> Gelman and Hill (2006) seem to leave a lot of this out--at least based on my
> skimming through it looking for discussion of priors.
>
> Thanks,
> Ned
>
>
>
>
> -----Original Message-----
> From: Ned Dochtermann [mailto:ned.dochtermann at gmail.com]
> Sent: Friday, May 20, 2011 5:44 PM
> To: 'r-sig-mixed-models at r-project.org'
> Subject: various priors for MCMCglmm
>
> Hi all,
>
> I have had and continue to have a lot of difficulty with not only the
> concept of priors but also their implementation for the MCMCglmm package.
> While Jarrod has always been extraordinarily helpful with this--as well as
> patient with those of us that seem eternally dense--I thought I'd list out
> some of the specifications I've come across to perhaps ease the frequency
> with which Jarrod has to reply to questions about priors.
>
> I've specified, for ease, R=G and a single random effect. From things I've
> read R is less sensitive to prior specification so this might be okay (?).
> Since I'm still not comfortable with priors hopefully these can be clarified
> by those more knowledgeable. I'm sure it would also be of general use if
> other priors were added via replies.
>
> The parts that are correct should be attributed to Jarrod. The parts that
> are wrong should be attributed to my clumsy attempts to generalize something
> he wrote. Some of this is just copied from posts to the listserv or Jarrod's
> course notes but I thought it might be useful to summarize then in a single
> place.
>
> Hopefully none of this is too misleading but will be of some use to others.
>
> Ned
>
> --
> Ned Dochtermann
> Department of Biology
> University of Nevada, Reno
>
> ned.dochtermann at gmail.com
> http://wolfweb.unr.edu/homepage/mpeacock/Ned.Dochtermann/
> http://www.researcherid.com/rid/A-7146-2010
> --
>
>
>
> #Inverse Wishart (univariate)
>
> 	prior.iw<-list(R=list(V=1, nu=1),G=list(G1=list(V=1, nu=1)))
>
> #Inverse Wishart (multivariate, variables=x)
>
> 	prior.miw<-list(R=list(V=diag(x), nu=x),G=list(G1=list(V=diag(x),
> nu=x)))
> #it came up in discussion that this prior can substantially affect the
> posterior when there are few data
>
> #I think that the following is an inverse Wishart for multiple response
> variables that is less informative is:
>
> 	prior.miw<-list(R=list(V=diag(x), nu=x, alpha.mu=c(0,0),
> alpha.V=diag(x)*a),G=list(G1=list(V=diag(x), nu=x, alpha.mu=c(0,0),
> alpha.V=diag(x)*a)))
>
> #for this a should be "something large (e.g. 1000, depending on the scale of
> the data)"
>
> #Inverse Gamma (univariate)
>
> 	prior.ig<-list(R=list(V=1, nu=0.002),G=list(G1=list(V=1, nu=0.002)))
>
> #Inverse Gamma (multivariate, two variables)
>
> 	prior.mig2<-list(R=list(V=diag(2),
> nu=1.002),G=list(G1=list(V=diag(2), nu=1.002)))
>
> #Inverse Gamma (multivariate, variables=x)
>
> 	prior.migX<-list(R=list(V=diag(x),
> nu=1.002),G=list(G1=list(V=diag(x), nu=1.002)))
>
> #or
>
> 	prior.migX<-list(R=list(V=diag(x),
> nu=b.002),G=list(G1=list(V=diag(x), nu=b.002)))
> #where b is x-1
>
> #I initially thought the first of these was the way to go but I'm less so
> now after looking at the
> #univariate specification. Also, Gelman (2006. Bayesian Analysis.
> 1(3):515-533) suggests that
> #there can be problems with this prior.
>
> #flat covariance between two responses
>
> 	prior.flatcor<-list(R=list(V=diag(2)*1e-6,
> nu=3),G=list(G1=list(V=diag(2)*1e-6, nu=3)))
> #to generalize this to x variables V would be diag(x) but I'm not sure if nu
> would be x+1
>
> #flat, uniform, prior for just a variance
>
> 	prior.flatvar<-list(R=list(V=1e-16, nu=-2),G=list(G1=list(V=1e-16,
> nu=-2)))
>
> #another flat improper prior, equivalent to REML fitting:
>
> 	prior.reml<-list(G=list(G1=list(V=1,nu=0)),R = list(V =1, nu = ))
>
> #I've actually run the same univariate analysis with prior.reml and lmer and
> gotten pretty much the same results
>
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>
>


-- 

Celine Teplitsky
Département Ecologie et Gestion de la Biodiversité UMR 7204
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