Back-transformation of Poisson model

Hi,

Obtianing the expected mean by integrating over the uncertainity (e.g. 
the posterior) gets a much better estimate

m1.mcmc<-MCMCglmm(y~1, random=~group, data=dat, prior=list(R=list(V=1, 
nu=0.002), G=list(G1=list(V=1, nu=0.002))), family="poisson")

hist(exp(m1.mcmc$Sol+ 0.5*rowSums(m1.mcmc$VCV)), breaks=100)
abline(v=mean(dat$y), col="red")

You might be able to improve on the REML estimate by subtracting 0.5*(Vi 
+Civ+0.25*Vv) before exponentiating. Vi is the samping variance of the 
intercept (standard error^2) Vv the sampling variance of the variance, 
and Civ the sampling covariance bewteen the two. Getting approximate 
values of Vv and Civ from glmer might be difficult though - not sure.

Cheers,

Jarrod

summary(m1)
exp(fixef(m1)+ 0.5*VarCorr(m1)$group[1])

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