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

In MCMCpack: Markov Chain Monte Carlo (MCMC) Package

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. \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.

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)

MCMCpack documentation built on Sept. 11, 2024, 8:13 p.m.