Monte Carlo Simulation from a Normal Likelihood (with known variance) with a Normal Prior
This function generates a sample from the posterior distribution of a Normal likelihood (with known variance) with a Normal prior.
MCnormalnormal(y, sigma2, mu0, tau20, mc = 1000, ...)
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 |
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.
An mcmc object that contains the posterior sample. This object can be summarized by functions provided by the coda package.
## 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)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.