**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!

Filed under: Books, R, Statistics, University life Tagged: Monte Carlo Statistical Methods

*Related*

To

**leave a comment** for the author, please follow the link and comment on their blog:

** Xi'an's Og » R**.

R-bloggers.com offers

**daily e-mail updates** about

R news and

tutorials on topics such as:

Data science,

Big Data, R jobs, visualization (

ggplot2,

Boxplots,

maps,

animation), programming (

RStudio,

Sweave,

LaTeX,

SQL,

Eclipse,

git,

hadoop,

Web Scraping) statistics (

regression,

PCA,

time series,

trading) and more...

If you got this far, why not

__subscribe for updates__ from the site? Choose your flavor:

e-mail,

twitter,

RSS, or

facebook...

**Tags:** Books, Monte Carlo Statistical Methods, R, statistics, University life