I am trying to sample from a posterior distribution using a MCMC algorithm using the Metropolis-Hastings sampler.
How should I deal with the situations where I'm stuck in regions of the posterior with zero probability?
These regions are present because the posterior distribution is truncated and also due to numerical limitations on the computer the likelihood can become zero if you are very far from the mean. That is, say the likelihood is distributed normally; if you are 100 standard deviations away from the mean you get what appears as zero probability to the computer.
What I want to know is how to chose the initial value of the chain in order to be sure that it is contained in the support of the posterior.