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#' Metropolis update for dyadic correlation with independent replicate data
#'
#' Metropolis update for dyadic correlation with independent replicate data.
#'
#'
#' @usage rrho_mh_rep(E.T, rho, s2 = 1)
#' @param E.T Array of square residual relational matrix series. The third
#' dimension of the array is for different replicates. Each slice of the array
#' according to the third dimension is a square residual relational matrix.
#' @param rho current value of rho
#' @param s2 current value of s2
#' @return a new value of rho
#' @author Peter Hoff, Yanjun He
#' @export rrho_mh_rep
rrho_mh_rep <-
function(E.T,rho,s2=1)
{
N<-dim(E.T)[3]
EM<-NULL
for (t in 1:N){
E<-E.T[,,t]
EM<-rbind(EM,cbind(E[upper.tri(E)],t(E)[upper.tri(E)] )/sqrt(s2))
}
emcp<-sum(EM[,1]*EM[,2])
emss<-sum(EM^2)
m<- nrow(EM)
sr<- 2*(1-cor(EM)[1,2]^2)/sqrt(m)
rho1<-rho+sr*qnorm( runif(1,pnorm( (-1-rho)/sr),pnorm( (1-rho)/sr)))
lhr<-(-.5*(m*log(1-rho1^2)+(emss-2*rho1*emcp)/(1-rho1^2)))-
(-.5*(m*log(1-rho^2 )+(emss-2*rho*emcp )/(1-rho^2 ))) +
( (-.5*log(1-rho1^2)) - (-.5*log(1-rho^2)) )
if(log(runif(1))<lhr) { rho<-rho1 }
rho
}
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