I was running MCMC for a while just in probability space. That didn't last long! It's tremendously useful to work in log probability space. It adds tremendous expressivity close to zero plus makes most multiplications sums. I think similar methods are probably used in other sectors.

What I found remarkable though was the big difference I saw in old versus new compilers with respect to the diversity of random numbers generated. I first thought that it was the entropy available on my system but that didn't turn out to be the key factor. So watch out for old compilers!