# simulate data
n=10
sigma2=1
x=rnorm(n)*sqrt(sigma2)

# initialize 
mu = mean(x)
s2=10
Sigma2 = NULL
Mu = NULL
nUpdates = 1000

# set some summary stats to simplify and speed sampler
xbar = mean(x)

for( i in 1:nUpdates ){
  # update sigma^2
  # propose candidate for sigma^2
  cand = s2*exp(rnorm(1)*.5)
  # account for proposal
  logR = log(cand/s2)
  # account for prior on sigma2
  logR = logR - log(cand/s2)
  # add in log-likelihood
  logR = logR + (-n/2)*log(cand) -0.5*sum((x-mu)^2)/cand -
                       ((-n/2)*log(s2) -0.5*sum((x-mu)^2)/s2 )
  if( logR>log(runif(1))) s2=cand

  # update mu
  cand = rnorm(1)+mu
  # log-likelihood
  logR =   -0.5*sum((x-cand)^2)/s2 -
                       (-0.5*sum((x-mu)^2)/s2 )
  if( logR>log(runif(1))) mu=cand
  # store values
  Mu=c(Mu,mu)
  Sigma2=c(Sigma2,s2)
}