chain information impacts summary statistics from coda

It seems chain information is not critical in mean, sd and quantiles; and not critical even for time series SE when convergence.

library(coda) 

x1 <- cbind(rnorm(100, 1, 1), rnorm(100,  1,1), rnorm(100,1 ,1 ),rnorm(100,1,1), cumsum(rnorm(100,1,1)))
x2 <- cbind(rnorm(100, 1,10), rnorm(100, 10,1), rnorm(100,10,10),rnorm(100,1,1), cumsum(rnorm(100,1,1)))
 
colnames(x1) <- colnames(x2) <- c('unequalSD','unequalMean','unequalboth','equal','autocorr')
 
o1 <- mcmc.list(mcmc(x1), mcmc(x2)) #maintain chain information. to add more chain: o1[[3]] <- mcmc(x3);
summary(o1)
 
summary(mcmc(rbind(x1,x2))) #no chain information

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