MCMCpack (version 1.7-0)

MCmultinomdirichlet: 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, ...)

Value

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

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. \(\pi\) is the parameter of interest of the multinomial distribution. It is of dimension \((d \times 1)\). We assume a conjugate Dirichlet prior:

$$\pi \sim \mathcal{D}irichlet(\alpha_0)$$

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

See Also

plot.mcmc, summary.mcmc

Examples

if (FALSE) {
## 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)
}