##### R code for the initial likelihood calculations 
##### in the AMI mortality case study (Lecture Notes, Day 1, Part 2)

n <- 400

s <- 72

bernoulli.likelihood <- function( theta, s, n ) {

  log.likelihood <- s * log( theta ) + ( n - s ) * log( 1 - theta )

  return( exp( log.likelihood ) )

}

theta.grid.1 <- seq( 0, 1, length = 500 )

likelihood.grid.1 <- bernoulli.likelihood( theta.grid.1, s, n )

par( mfrow = c( 1, 2 ) )

plot( theta.grid.1, likelihood.grid.1, type = 'l', xlab = 'theta',
  ylab = 'Likelihood Function' )

theta.grid.2 <- seq( 0.12, 0.25, length = 500 )

likelihood.grid.2 <- bernoulli.likelihood( theta.grid.2, s, n )

plot( theta.grid.2, likelihood.grid.2, type = 'l', xlab = 'theta',
  ylab = 'Likelihood Function' )

par( mfrow = c( 1, 1 ) )

bernoulli.log.likelihood <- function( theta, s, n ) {

  log.likelihood <- s * log( theta ) + ( n - s ) * log( 1 - theta )

  return( log.likelihood )

}

log.likelihood.grid.1 <- bernoulli.log.likelihood( theta.grid.2, s, n )

plot( theta.grid.2, log.likelihood.grid.1, type = 'l', xlab = 'theta',
  ylab = 'Log Likelihood Function' )