MCmultinomdirichlet | R Documentation |
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.
\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.
An mcmc object that contains the posterior sample. This object can be summarized by functions provided by the coda package.
plot.mcmc
, summary.mcmc
## 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)
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