MCMCpack (version 1.7-1)

MCnormalnormal: 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, ...)

Value

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

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. \(\mu\) is the parameter of interest of the Normal distribution. We assume a conjugate normal prior:

$$\mu \sim \mathcal{N}(\mu_0, \tau^2_0)$$

\(y\) is a vector of observed data.

See Also

plot.mcmc, summary.mcmc

Examples

if (FALSE) {
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"))
}