MCMCpack (version 1.7-1)

MCpoissongamma: Monte Carlo Simulation from a Poisson Likelihood with a Gamma Prior

Description

This function generates a sample from the posterior distribution of a Poisson likelihood with a Gamma prior.

Usage

MCpoissongamma(y, alpha, beta, 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 counts (must be non-negative).

alpha

Gamma prior distribution shape parameter.

beta

Gamma prior distribution scale parameter.

mc

The number of Monte Carlo draws to make.

...

further arguments to be passed

Details

MCpoissongamma directly simulates from the posterior distribution. This model is designed primarily for instructional use. \(\lambda\) is the parameter of interest of the Poisson distribution. We assume a conjugate Gamma prior:

$$\lambda \sim \mathcal{G}amma(\alpha, \beta)$$

\(y\) is a vector of counts.

See Also

plot.mcmc, summary.mcmc

Examples

if (FALSE) {
data(quine)
posterior <- MCpoissongamma(quine$Days, 15, 1, 5000)
summary(posterior)
plot(posterior)
grid <- seq(14,18,0.01)
plot(grid, dgamma(grid, 15, 1), type="l", col="red", lwd=3, ylim=c(0,1.3),
  xlab="lambda", ylab="density")
lines(density(posterior), col="blue", lwd=3)
legend(17, 1.3, c("prior", "posterior"), lwd=3, col=c("red", "blue"))
}