Which Coin?

Create three coins, one fair and two biased:

theta_coin1 <- 0.4
theta_coin2 <- 0.5
theta_coin3 <- 0.6

coin_df <- tibble(
  model = factor(c("coin1", "coin2", "coin3")),
  prior = rep(1/3, 3)
)

Randomly select one of them but keep its identity secret:

theta <- sample(c(theta_coin1, theta_coin2, theta_coin3), 1)

Flip it 5 times and report the number of heads:

flips <- sample(c(0, 1), 5, replace = TRUE, prob = c(1 - theta, theta))
heads <- sum(flips)
heads

## [1] 1

Use this information to calculate likelihoods:

# coin1:
replications <- replicate(
  50000, 
  sum(sample(c(0, 1), 5, replace = TRUE, prob = c(1 - theta_coin1, theta_coin1)))
)
likelihood_coin1 <- mean(replications == heads)

# coin2:
replications <- replicate(
  50000, 
  sum(sample(c(0, 1), 5, replace = TRUE, prob = c(1 - theta_coin2, theta_coin2)))
)
likelihood_coin2 <- mean(replications == heads)

# coin3:
replications <- replicate(
  50000, 
  sum(sample(c(0, 1), 5, replace = TRUE, prob = c(1 - theta_coin3, theta_coin3)))
)
likelihood_coin3 <- mean(replications == heads)

coin_df$likelihood <- c(likelihood_coin1, likelihood_coin2, likelihood_coin3)

Update your belief about which coin is being flipped:

coin_df$product <- coin_df$prior * coin_df$likelihood
coin_df$posterior <- coin_df$product / sum(coin_df$product)
coin_df

## # A tibble: 3 x 5
##    model     prior likelihood    product posterior
##   <fctr>     <dbl>      <dbl>      <dbl>     <dbl>
## 1  coin1 0.3333333    0.25770 0.08590000 0.5232487
## 2  coin2 0.3333333    0.15816 0.05272000 0.3211371
## 3  coin3 0.3333333    0.07664 0.02554667 0.1556142

Repeat.