I\'m trying to make a stacked bar plot in R with error bars for a value that I want to predefine, rather than calculate, but each bar has a different value.
For example
First, add the upper and lower bounds to your mx dataframe:
library(dplyr)
mx <- mx %>% group_by(Period) %>%
  mutate(pos = cumsum(value)) %>%
  ungroup() %>%
  mutate(ci = c(.5, .1, .2, .2),
         upper = pos + ci/2,
         lower = pos - ci/2)
Then, add a geom_errorbar to your plot:
ggplot(mx, aes(x=Period, y=value, fill=variable), xLabels=NA) +
  geom_bar(stat="identity") +
  geom_errorbar(aes(ymin = lower, ymax = upper), width = .2, col = "red") +
  facet_grid(~Sample) +
  scale_fill_manual(values = c("grey69","black")) +
  theme_bw() +
  xlab("") + 
  ylab ("")