Metropolis Algorithm

Taken from: _https://darrenjw.wordpress.com/2010/08/15/metropolis-hastings-mcmc-algorithms/_

The data generation AKA innovations function.

metrop1=function(n=1000,eps=0.5) 
{
        vec=vector("numeric", n)
        x=0
        vec[1]=x
        for (i in 2:n) {
                innov=runif(1,-eps,eps)
                #notice the acceptance ratio = minus eps over eps.
                can=x+innov
                aprob=min(1,dnorm(can)/dnorm(x))
                u=runif(1)
                if (u < aprob) 
                        x=can
                vec[i]=x
        }
        vec
}

Plotting:

plot.mcmc<-function(mcmc.out)
{
    op=par(mfrow=c(2,2))
    plot(ts(mcmc.out),col=2)
    hist(mcmc.out,30,col=3)
    qqnorm(mcmc.out,col=4)
    abline(0,1,col=2)
    acf(mcmc.out,col=2,lag.max=100)
    par(op)
}
 
metrop.out<-metrop1(10000,1)
plot.mcmc(metrop.out)