metropolis = function (start=1, n=100, sig.q=1, mu.p=0, sig.p=1) {

#starting value theta_0 = start
#run for n iterations

  #set up vector theta[] for the samples
  theta=rep(NA,n)
  theta[1]=start

  #count the number of accepted proposals
  accept=0

  #Main loop
  for (t in 2:n) {

    #pick a candidate value theta* from N(theta[t-1], sig.q)
    theta.star = rnorm(1, theta[t-1], sqrt(sig.q))
    
    #generate a random number between 0 and 1:
    u = runif(1)

    # calculate acceptance probability:
    r = (dnorm(theta.star,mu.p,sig.p)) / (dnorm(theta[t-1],mu.p,sig.p) )
    
    a=min(r,1)
    

    #if u<a we accept the proposal; otherwise we reject
    if (u<a) {   
        #accept
            accept=accept+1
            theta[t] = theta.star
    }
    else {
        #reject
        theta[t] = theta[t-1]
        }
  #end loop
  }