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.
\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.
See Also
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)