Examples of prior having impact on posterior

471238_prior_vs_posterior.R

# code accompanying answer: https://stats.stackexchange.com/a/471245/35989

n <- 22
x <- 13

lik <- function(p) dbinom(x, n, p) * 20
prior <- function(p) dbeta(p, alpha, beta)
post <- function(p) dbeta(p, alpha+x, beta+(n-x))

op <- par(mfrow=c(1,3), mar=c(3,1,1,1), cex=0.9)

for (prior_size in c(5, 25, 100)) {  
  prior_prob <- 0.3
  alpha <- prior_prob * prior_size
  beta <- (1-prior_prob) * prior_size
  
  plot(NA, ylim=c(0,9), xlim=c(0,1), axes=FALSE, xlab="", ylab="")
  curve(lik, 0, 1, add=TRUE, col="red", axes=FALSE, xlab="", ylab="", ylim=5)
  curve(post, 0, 1, add=TRUE, col="violet")
  curve(prior, 0, 1, add=TRUE, col="blue")
  axis(1)
  legend("topright", legend=c("prior", "likelihood", "posterior"),
         lty=1, col=c("blue", "red", "violet"), bty="n")
}

par(op)