MCbinomialbeta: Monte Carlo Simulation from a Binomial Likelihood with a Beta Prior

Description

This function generates a sample from the posterior distribution of a binomial likelihood with a Beta prior.

Usage

MCbinomialbeta(y, n, alpha = 1, beta = 1, mc = 1000, ...)

Arguments

The number of successes in the independent Bernoulli trials.

The number of independent Bernoulli trials.

alpha

Beta prior distribution alpha parameter.

beta

Beta prior distribution beta parameter.

The number of Monte Carlo draws to make.

...

further arguments to be passed

Value

An mcmc object that contains the posterior sample. This object can be summarized by functions provided by the coda package.

Details

MCbinomialbeta directly simulates from the posterior distribution. This model is designed primarily for instructional use. $\pi$ is the probability of success for each independent Bernoulli trial. We assume a conjugate Beta prior:

$$\pi \sim \mathcal{B}eta(\alpha, \beta)$$

$y$ is the number of successes in $n$ trials. By default, a uniform prior is used.

Examples

Run this code

# NOT RUN {
# }
# NOT RUN {
posterior <- MCbinomialbeta(3,12,mc=5000)
summary(posterior)
plot(posterior)
grid <- seq(0,1,0.01)
plot(grid, dbeta(grid, 1, 1), type="l", col="red", lwd=3, ylim=c(0,3.6),
  xlab="pi", ylab="density")
lines(density(posterior), col="blue", lwd=3)
legend(.75, 3.6, c("prior", "posterior"), lwd=3, col=c("red", "blue"))
# }
# NOT RUN {
# }