R: Monte Carlo Simulation from a Normal Likelihood (with known...

MCnormalnormal {MCMCpack} | R Documentation

## Monte Carlo Simulation from a Normal Likelihood (with known variance) with a Normal Prior

### Description

This function generates a sample from the posterior distribution of a Normal likelihood (with known variance) with a Normal prior.

### Usage

    MCnormalnormal(y, sigma2, mu0, tau20, mc = 1000, ...)

### Arguments

`y` | The data.
`sigma2` | The known variance of y.
`mu0` | The prior mean of mu.
`tau20` | The prior variance of mu.
`mc` | The number of Monte Carlo draws to make.
`...` | further arguments to be passed

### Details

`MCnormalnormal` directly simulates from the posterior distribution. This model is designed primarily for instructional use. μ is the parameter of interest of the Normal distribution. We assume a conjugate normal prior:

μ \sim \mathcal{N}(μ_0, τ^2_0)

y is a 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

`plot.mcmc`, `summary.mcmc`

### Examples

    ## Not run:
    y <- c(2.65, 1.80, 2.29, 2.11, 2.27, 2.61, 2.49, 0.96, 1.72, 2.40)
    posterior <- MCMCpack:::MCnormalnormal(y, 1, 0, 1, 5000)
    summary(posterior)
    plot(posterior)
    grid <- seq(-3,3,0.01)
    plot(grid, dnorm(grid, 0, 1), type="l", col="red", lwd=3, ylim=c(0,1.4),
       xlab="mu", ylab="density")
    lines(density(posterior), col="blue", lwd=3)
    legend(-3, 1.4, c("prior", "posterior"), lwd=3, col=c("red", "blue"))

    ## End(Not run)

[Package MCMCpack version 1.5-0 Index]