# Exercise 2 - mcmc sampling
# Author Roland Krause

scale = 2.5
sigma = 10
proposal <- function(x, sigma) {
	rnorm(1,x,sigma)
}
target <- function(x) { (0.3 * exp(-0.2 *x ^ 2 ) + 0.7 * exp(-0.2 * (x-10)^2))/scale}

accept_ratio <- function(x, xi){
	min(1, target(xi)/target(x))
}

N = 10

x = proposal(1,1)

sample <-function(N, sigma){
	final_dist =c()
	for (i in c(1:N)){
		u = runif(1)
		xi = proposal(x, sigma)
		a = accept_ratio(x,xi)
				
		if (u<=a){
		   x = xi
		}	
		final_dist[i] = x
	
	
}
	return(final_dist)		
}
par(mfcol=c(2,4))
for (sigma in c(1,10,100,1000)){

chain = sample(5000, sigma)
plot(chain, xlab="iteration", ylab="samples", main=paste(c("Sigma ", sigma)))
hist(chain, freq=FALSE, xlab="samples", ylim=c(0,0.4), ylab="Frequency",xlim=c(-5,15), main=paste(c("Sigma ", sigma)))
plot(target, xlim=c(-5,15), xlab="x", ylab="xi", add=TRUE, col="red")
}