require("ggplot2")
require("svglite")

n <- c(10, 100)
p <- seq(0, 1, 0.01)
mat <- expand.grid(n, p)
colnames(mat) <- c("n", "p")

get_jeffreys_ci <- function(number_of_successes, total_number, ci_width = .95) {
  result <- qbeta(
    p = c((1 - ci_width) / 2, (1 / 2) + (ci_width / 2)),
    shape1 = number_of_successes + 1 / 2,
    shape2 = total_number - number_of_successes + 1 / 2
  )

  if (number_of_successes == 0) {
    result[1] <- 0
  } else if (number_of_successes == total_number) {
    result[2] <- 1
  }

  result
}

tmp <- apply(
  mat,
  MARGIN = 1,
  function(x) {
    ret <- get_jeffreys_ci(x[2] * x[1], x[1])
    c(ret[1], ret[2])
  }
)

mat[, "ci_lb"] <- t(tmp)[, 1]
mat[, "ci_ub"] <- t(tmp)[, 2]
mat[, "logit_p"] <- log(mat$p / (1 - mat$p))

mat <- as.data.frame(mat)

ggplot(
  mat,
  aes(
    x = logit_p
  )
) +
  geom_hline(yintercept = 0.5, linetype = "dotted", alpha = .5) +
  geom_vline(xintercept = 0, linetype = "dotted", alpha = .5) +
  annotate(geom = "text", x = 1.0, y = 0.43, label = "n = 10", hjust = -0.1) +
  annotate(geom = "text", x = 0.3, y = 0.48, label = "n = 100", hjust = -0.1) +
  geom_line(aes(y = p)) +
  geom_line(aes(y = ci_lb, linetype = factor(n)), colour = "purple") +
  geom_line(aes(y = ci_ub, linetype = factor(n)), colour = "purple") +
  xlab("logit(p)") +
  see::theme_modern() +
  theme(
    legend.position = "none"
  )

ggsave(
  "out.svg",
  units = "px",
  height = 496 * 4,
  width = 800 * 4
)