minfconf=function(x,y){

#this will spit out the quantiles of the MI from the bootstrap..

library(sm)

air3  = cbind(x,y)
result.12 = sm.density(air3,   eval.points = air3,   display = "none")
result.1  = sm.density(x,  eval.points = x,  display = "none")
result.2  = sm.density(y, eval.points = y, display = "none")

#Mutual Information from the hand out..
#tobs = mean(log(result.12$estimate /(result.1$estimate * result.2$estimate)))

#Average Mutual Information .. Moon et al. (1995)
tobs = sum(result.12$estimate * log2(result.12$estimate /(result.1$estimate * result.2$estimate)))

print(c(tobs))


n=length(x)
nsim   = 150
#500 bootstrap samples..

#vector of MI for the bootstrap samples..
simval = rep(0,nsim)

#vector of correlations of the bootstrap samples..
simcor=rep(0,nsim)

for (i in 1:nsim) {

#sample y but not x. This disturbs the joint occurrence of x and y
xy=sample(y,replace=TRUE)

   samp = cbind(y1 = x, y2 = xy)	

#to obtain confidence interval of MI both x and y are undisturbed.
#xn=sample(1:n, replace=TRUE)
#   samp = cbind(y1 = x[xn], y2 = y[xn])	

   result.12 = sm.density(samp,     eval.points = samp,     display = "none")
   result.1  = sm.density(samp[,1], eval.points = samp[,1], display = "none")
   result.2  = sm.density(samp[,2], eval.points = samp[,2], display = "none")

#Mutual Information from the hand out..
#simval[i]      = mean(log(result.12$estimate /(result.1$estimate * result.2$estimate)))

#Average Mutual Information .. Moon et al. (1995)
simval[i]     = sum(result.12$estimate * log2(result.12$estimate /(result.1$estimate * result.2$estimate)))

simcor[i]=cor(samp[,1],samp[,2])
   }

quantile(simval,c(0.05,0.1,.50,.90,.95))
quantile(simcor,c(0.05,0.1,.50,.90,.95))

par(mfrow=c(1,2))

zz=boxplot(simcor,ylim=range(simcor,cor(x,y)),xlab="",ylab="Cor",plot=F)
zz$names=rep("",length(zz$names))
z1=bxp(zz,xlab="",ylab="Cor",ylim=range(simcor,cor(x,y)), cex=1.25)
points(z1, cor(x,y),cex=1.5,pch=16)
title(main="Boxplot of bootstrap correlations")

zz=boxplot(simval,ylim=range(simval,tobs),xlab="",ylab="MI",plot=F)
zz$names=rep("",length(zz$names))
z1=bxp(zz,xlab="",ylab="MI",ylim=range(simval,tobs),cex=1.25)
points(z1, tobs,cex=1.5,pch=16)
title(main="Boxplot of bootstrap MI")

}