# MCmultinomdirichlet: Monte Carlo Simulation from a Multinomial Likelihood with a... In MCMCpack: Markov Chain Monte Carlo (MCMC) Package

 MCmultinomdirichlet 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. \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.

### Value

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

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)



MCMCpack documentation built on May 29, 2024, 11:23 a.m.