R: Monte Carlo Simulation from a Multinomial Likelihood with a...

MCmultinomdirichlet {MCMCpack} | R Documentation

## Monte Carlo Simulation from a Multinomial Likelihood with a Dirichlet Prior

### Description

This function generates a sample from the posterior distribution of a multinomial likelihood with a Dirichlet prior.

### Usage

    MCmultinomdirichlet(y, alpha0, mc = 1000, ...)

### Arguments

`y` | A vector of data (number of successes for each category).
`alpha0` | The vector of parameters of the Dirichlet prior.
`mc` | The number of Monte Carlo draws to make.
`...` | further arguments to be passed

### Details

`MCmultinomdirichlet` directly simulates from the posterior distribution. This model is designed primarily for instructional use. π is the parameter of interest of the multinomial distribution. It is of dimension (d \times 1). We assume a conjugate Dirichlet prior:

π \sim \mathcal{D}irichlet(α_0)

y is a (d \times 1) vector of observed data.

### 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:
    ## Example from Gelman, et. al. (1995, p. 78)
    posterior <- MCmultinomdirichlet(c(727,583,137), c(1,1,1), mc=10000)
    bush.dukakis.diff <- posterior[,1] - posterior[,2]
    cat("Pr(Bush > Dukakis): ",
       sum(bush.dukakis.diff > 0) / length(bush.dukakis.diff), "\n")
    hist(bush.dukakis.diff)

    ## End(Not run)

[Package MCMCpack version 1.5-0 Index]