R: Monte Carlo Simulation from a Poisson Likelihood with a Gamma...

MCpoissongamma {MCMCpack} | R Documentation

## 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, ...)

### 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. λ is the parameter of interest of the Poisson distribution. We assume a conjugate Gamma prior:

λ \sim \mathcal{G}amma(α, β)

y is a vector of counts.

### Value

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

### See Also

`plot.mcmc`, `summary.mcmc`

### Examples

    ## Not run:
    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"))

    ## End(Not run)

[Package MCMCpack version 1.6-3 Index]