Examples of uninformative beta priors for binomial distribution

uninformative-beta-priors-example.R

priors <- c(0, 0.001, 0.333, 0.5, 1)

s <- c(0, 1, 1, 5, 5)
f <- c(1, 1, 2, 1, 25)



dbeta2 <- function(x, prior1, prior2 = prior1) {
  if (prior1 == 0)
    x^-1 * (1-x)^-1
  else
    dbeta(x, prior1, prior2)
}



pardef <- par(mfrow = c(length(s)+1, length(priors)), mar = c(2,1.5,2,1.5))

for (i in seq_along(priors)) {
  curve(dbeta2(x, priors[i]), 0, 1, n = 1001, xlab = "", ylab = "",
        axes = FALSE, col = "lightblue", lwd = 2)

  title(substitute(list(paste(alpha == x), paste(beta == y)),
                   list(x = priors[i], y = priors[i])))

  legend("bottomright", "y=0,\nn=0",
         bty = "n")

  axis(1, at = c(0, 0.5, 1))
}

for (j in seq_along(s)) {

  for (i in seq_along(priors)) {

    curve(dbeta(x, s[j] + priors[i], f[j] + priors[i]), 0, 1,
          n = 1001, xlab = "", ylab = "", axes = FALSE,
          col = "lightblue", lwd = 2)
    axis(1, at = c(0, 0.5, 1))
    legend("bottomright", paste0("y=", s[j], "\nn=", s[j]+f[j]),
           bty = "n")
  }

}

par(pardef)