met<-function(pi,proposal,X0, n, s)
{
output<-c(X0)
x<-X0
for (i in 1:n)
{
y<-x + s * proposal(1)
u<-runif(1)
if (log(pi(y)/pi(x)) > log(u))
(x<-y)
output<-c(output,x)
}
output
}
metGauss<-function(proposal,X0, n, s)
{
output<-c(X0)
x<-X0
for (i in 1:n)
{
y<-x + s * proposal(1)
u<-runif(1)
if ((x^2 - y^2)/2 > log(u))
(x<-y)
output<-c(output,x)
}
output
}
opt.sca_function()
{
z<-rep(0,100)
a<-rep(0,100)
s<-rep(0,100)
for (i in 1:20)
{
s[i]<-1+ (i-1)/5
x<-met(dnorm,rnorm,0,10000,s[i])
z[i]<-sum((x[1:3999]-x[2:4000])^2)
a[i]<-acceptance.rate(x)
}
par(mfcol=c(1,2))
plot(s,z)
plot(a,z)
par(mfcol=c(1,1))
}

acceptance.rate<-function(x)
{
k<-length(x)
number<-c(k-1)
for (i in 1:(k-1))
{
if (x[i]==x[i+1])
(number<-number-1)
}
number/(k-1)
}
determplots<-function(n,x,proposal)
{
k<-length(x)
y<-metGauss(proposal,x[1],n,2.4)
plot(y,type="l",ylim=c(-5,max(x)*1.1))
for (i in 2:k)
{
y<-metGauss(proposal,x[i],n,2.4)
points(y,type="l")
}
}
independence.sampler<-function(lambda, X0, n)
{
output<-c(X0)
x<-X0
for (i in 1:n)
{
y<- rexp(1)/lambda 
u<-runif(1)
if ((x-y)*(1-lambda ) > log(u))
(x<-y)
output<-c(output,x)
}
output
}
clt.i.s<-function(m,lambda)
{
z_rep(0,m)
for (i in 1:m)
z[i]<-mean(independence.sampler(lambda,1,10000))
z
}