library(metafor)
library(metaBMA)

nsims <- 100
cover <- matrix(0, nrow = 100, 2)
colnames(cover) <- c("freq", "bayes")
tau = 0.1

for(i in 1:nsims) {
  print(i)
  y <- data.frame(
    # generating data for a population d = 0.5 and a given tau
    effsize = rnorm(6, 0.2, tau),
    SE = runif(6, 0.05, 0.1),
    study = 1:6)

  # fitting a frequentist random-effect meta-analysis model
  fit_freq <- rma(effsize, sei = SE, data = y, method = "PM")

  lower_freq <- confint(fit_freq, level = .95)$random[2, 2]
  upper_freq <- confint(fit_freq, level = 0.95)$random[2, 3]

  #fitting a Bayesian random-effect meta-analysis model
   fit_bayes <- meta_random(
     y$effsize, y$SE, y$study,
     d = "norm", d.par = c(0, 10000),
     tau = "halfcauchy", tau.par = 10000,
     sample = 500, summarize = "jags"
   )
  #
  # lower_bayes <- fit_bayes$estimates[2, 6]
  # upper_bayes <- fit_bayes$estimates[2, 7]



  cover[i,] <- c(ifelse(lower_freq < tau && upper_freq > tau, 1, 0),
                 ifelse(fit_bayes$estimates[2,4] < tau && fit_bayes$estimates[2,5] > tau, 1, 0))

  # res[i, ] <- cbind(lower_freq, upper_freq, lower_bayes, upper_bayes)

}

colMeans(cover)