Nothing
R.hat <- function (M, burn.in = 0.5) {
alpha = .05 # 95% intervals
m = ncol(M)
x = M [round(((burn.in * nrow(M)) + 1), 0):nrow(M),] # second half of simulated sequences h <- round(((burn.in * n) + 1), 0)
n = nrow(x)
xdot = as.vector(apply(x, 2, mean))
s2 = as.vector(apply(x, 2, var))
W = mean(s2)
B = n*var(xdot)
muhat = mean(xdot)
varW = var(s2)/m
varB = B^2 * 2/(m-1)
covWB = (n/m)*(cov(s2,xdot^2) - 2*muhat*cov(s2,xdot))
sig2hat = ((n-1)*W + B)/n
quantiles = quantile (as.vector(x), probs=c(.025,.25,.5,.75,.975))
if (W > 1.e-8) { # non-degenerate case
postvar = sig2hat + B/(m*n)
varpostvar =
(((n-1)^2)*varW + (1+1/m)^2*varB + 2*(n-1)*(1+1/m)*covWB)/n^2
chisqdf <- function(A, varA) 2 * (A^2/varA)
post.df = chisqdf (postvar, varpostvar)
post.range = muhat + sqrt(postvar) * qt(1-alpha/2, post.df)*c(-1,0,1)
varlo.df = chisqdf (W, varW)
confshrink = sqrt(postvar/W*(post.df+3)/(post.df+1))
confshrink
}
else { # degenerate case: all entries in "data matrix" are identical
1
}
}
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