Using beta-distributed interval-censored data to produce an estimate for the median share of US adults having taken the vaccine by end of Q2 2021.

beta_interval_data.R

library(tidyverse)
library(fitdistrplus)
dplyr::select -> select
.Machine$double.eps -> eps
1975 -> N # number of responses

tibble(lower = c(0, 0.25, 0.5, 0.75), # lower bins
       upper = c(0.25 + eps, 0.5 + eps, 0.75 + eps, 1), # upper bins
       pct = c(0.32, 0.51, 0.15, 1 - sum(0.32, 0.51, 0.15)), # response shares
       n = floor(pct * N)) %>% # implied responses + eps
  mutate(data = pmap(list(lower, upper, n), function(...) {
    dots <- list(...)
    sample_n(tibble(left = dots[[1]], right = dots[[2]]), size = dots[[3]], replace = TRUE)
  })) %>%
  select(data) %>% unnest(cols = c(data)) %>% as.data.frame() %>%
  # use the quantile function to find the % at which half of chance is on either side (the median).
  fitdistcens("beta") %>% # this is interval-censored beta data
  coef() %>%
  { qbeta(0.5, .[[1]], .[[2]]) }
  
0.3279981

# folks believe a third of US adults will have taken the vaccine by the end of Q2 2021