<br/>
My question originated from yesterdays Xi'an [suggestion][1] to check integrability against the posterior posterior in my nonlinear hierarhical model. I did not checked it, but had possible infinity in mind and found out that one of my conditionals (which is inverse gamma distribution) have infinite variance. So that sampling resulted in chains often being far away at the tails. <br/>
So, this rised a question for me: <br/>
How to sample to properly sample from distributions with infinite variances like inverse gamma distribution (with $ \alpha = 2 $) or Levy distribution or any other distribution with infinite variance? What does MCMC could offer? I tried to search for papers dealing with such issues, but still no luck.


  [1]: http://stats.stackexchange.com/questions/23218/posterior-mean-of-exponential-functions-how-to-do-it-with-mcmc