#source("c:/Work07/ShortCourse07/Programs/MultivariateTruncatedIS.txt",print.eval=TRUE)#
#This gives an importance sampling algorithm for a Truncated Normal#
#-------------------Does Multivatiate Tail Probabilities------------------------
library(MASS)
p<-5			#dimension of MVN
mu<-c(0,0,0,0,0)	#mean of MVN
S=c(1,.2,.3,.4,.5,.2,1,.2,.5,.3,.3,.2,1,.2,.4,.4,.5,.2,1,.3,.5,.3,.4,.3,1)
S<-array(S,dim=c(5,5))	#covariance matrix
a<-c(2,3,1,2,1)	#Cutoff  Point
#----------------------Preliminary Calcualtiona---------------------------------
dS<-det(S)
iS<-ginv(S)
#----------------------Importance Sampling--------------------------------------
nsim<-5000		#Number of simulations
Prob<-array(0,dim=c(nsim,1))
for(i in 1:nsim)
{
  x<-a+rexp(p)
  Prob[i]<-exp(-t(x-mu)%*%iS%*%(x-mu)/2)/prod(dexp(x-a))
}
Prob<-Prob/((2*pi*dS)^(p/2))
print(mean(Prob))
plot(cumsum(Prob)/c(1:nsim),lwd=2,type="l")