R: Monte Carlo Simulation from a Binomial Likelihood with a Beta...

MCbinomialbeta {MCMCpack} | R Documentation

## 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

`y` | The number of successes in the independent Bernoulli trials.
`n` | The number of independent Bernoulli trials.
`alpha` | Beta prior distribution alpha parameter.
`beta` | Beta prior distribution beta parameter.
`mc` | The number of Monte Carlo draws to make.
`...` | further arguments to be passed

### Details

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

π \sim \mathcal{B}eta(α, β)

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

### Value

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

### See Also

`plot.mcmc`, `summary.mcmc`

### Examples

    ## 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"))

    ## End(Not run)

[Package MCMCpack version 1.6-3 Index]