Bayesian Inference Exercises Using R
I.
1: Coin Toss Posterior
A coin is tossed 12 times and 8 heads are observed. Prior distribution: Beta(2,2). Find the posterior
distribution.
R code:
alpha <- 2
beta <- 2
heads <- 8
tails <- 4
posterior_alpha <- alpha + heads
posterior_beta <- beta + tails
posterior_alpha
posterior_beta
2. Use the posterior from Exercise 1 to compute the posterior mean.
R code:
alpha <- 10
beta <- 6
posterior_mean <- alpha/(alpha+beta)
posterior_mean
3. Generate 5000 posterior samples.
R code:
samples <- rbeta(5000,10,6)
mean(samples)
