Monte Carlo Simulation from a Multinomial Likelihood with a Dirichlet Prior
This function generates a sample from the posterior distribution of a multinomial likelihood with a Dirichlet prior.
MCmultinomdirichlet(y, alpha0, mc = 1000, ...)
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 |
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.
An mcmc object that contains the posterior sample. This object can be summarized by functions provided by the coda package.
## 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)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.