# Bounded target support

**Xi'an's Og » R**, and kindly contributed to R-bloggers]. (You can report issue about the content on this page here)

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**H**ere is an interesting question from Tomàs that echoes a lot of related emails:

I’m turning to you for advice. I’m facing problem where parameter space is bounded, e.g. all parameters have to be positive.

If in MCMC as proposal distribution I use normal distribution, then at some iterations I get negative proposals. So my question is: should I use recalculation of acceptance probability every time I reject the proposal (something like in delayed rejection method), or I have to use another proposal (like lognormal, trancated normal, etc.)?

**I**t is indeed a popular belief that something needs to be done to counteract restricted supports. However, there is no mathematical reason for doing so! Consider the following illustration

target=function(x) (x>0)*(x<1)*dnorm(x,mean=4) mcmc=rep(0.5,10^5) for (t in 2:10^5){ prop=mcmc[t-1]+rnorm(1,.1) if (runif(1)<target(prop)/target(mcmc[t-1])) mcmc[t]=prop else mcmc[t]=mcmc[t-1] } hist(mcmc,prob=TRUE,col="wheat",border=FALSE,main="",xlab="") curve(dnorm(x-4)/(pnorm(-3)-pnorm(-4)),add=TRUE,col="sienna",lwd=2)

and the following outcome, with a perfect fit!

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