Tomas Iesmantas writes:
I’m facing a 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, truncated normal, etc.)?
The simplest solution is to just calculate p(theta)=0 for theta outside the legal region, thus reject those jumps. This will work fine (just remember that when you reject, you have to stay at the last value for one more iteration), but if you’re doing these rejections all the time, you might want to reparameterize your space, for example using logs for positive parameters, logits for constrained parameters, and softmax for parameters that are constrained to sum to 1.