Maximum likelihood estimation of the success probability on a Bernoulli experiment in R.

bernoulli_mle.R

library(microbenchmark)

bernoulli.loglik.derivative <- function(p, dat)
{
  -(sum(dat) - length(dat) * p)
}

optim <- function(dat)
{
  p.hat <- 1
  for (i in seq(10000))
  {
    p.hat <- p.hat - 0.0001 * bernoulli.loglik.derivative(p.hat, dat)
  }
  p.hat
}

dat <- sample(0:1, 10000, prob=c(.25, .75), replace=TRUE)
print(mean(dat))
print(optim(dat))
res <- microbenchmark(f=optim(dat))
print(res)