[R-sig-ME] horseshoe priors in MCMCglmm?

[Jarrod Hadfield]

Hi,

I could be wrong, but it looks like the horseshoe prior is a mixture of 
normals, whose standard deviations are drawn from a scaled 1-df Cauchy 
distribution.

Since 1-df Cauchy is equal to the 1-df t, and t^2 is equal to the F, 
isn't this just the same as treating each `fixed' effect as a random 
effect and using a parameter expended prior? You could trick MCMCglmm 
into doing this ...

dat<-data.frame(y=rnorm(100), x1=rnorm(100), x2=rnorm(100))

prior<-list(R=list(V=1, nu=0), G=list(G1=list(V=diag(2), nu=1, 
alpha.mu=c(0,0), V=diag(2)*100)))
# Horseshoe priors on x1 and x2 with scale=100 ?????

m1<-MCMCglmm(y~1, random=~idh(x1+x2):trait, pr=T, data=dat, prior=prior)

summary(m1, random=TRUE)

I haven't got time to check the logic thoroughly, but it might be worth 
investigating.

Cheers,

Jarrod

On 21/02/16 21:09, Jonathan Judge wrote:
> Certain authors have been reporting impressive shrinkage performance from incorporation of the so-called "horseshoe" (http://www.jmlr.org/proceedings/papers/v5/carvalho09a/carvalho09a.pdf)  and "horseshoe plus" (http://arxiv.org/pdf/1502.00560v2.pdf) priors into their MCMC sampling.
>
> I've seen a fair amount of attention to incorporating these into Stan programming, but I still prefer to use MCMCglmm at times, particularly with large groups.  Has anyone successfully incorporated any of the horseshoe priors for usage in MCMCglmm, through parameter expansion or otherwise?
>
> Warm regards,
> Jonathan
>
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>
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