Gaussian scale mixture seems to be a good tool for modeling heavytailed residual in regression. I wonder if there is a systematic way to fit Gaussian scale mixture to data ? It appears that expectationmaximization algorithm only works for fitting locationscale mixture distribution, is that correct? asked Aug 19 '11 at 14:52 Li Tang 
Here's an answer to a slightly different question. There exists ways of more directly defining a heavy tailed distribution other than using a mixture of gaussians (which are inherently not heavytailed). The challenge in the past has been efficient/compact representation, as well as learning/inference. There has been some work recently to address these issues, e.g., http://www.select.cs.cmu.edu/publications/paperdir/nips10bicksonguestrin.pdf This might better solve whatever problem it is you have. answered Aug 20 '11 at 14:37 Yisong Yue Thanks for your response. But the class of Gaussian scale mixture distributions contains many widely used heavytail distributions, e.g., the symmetric stable distributions and Laplace distributions. In fact, in the work you mentioned, "Inference with Multivariate HeavyTails in Linear Models", the authors assume that all observation nodes of their model are distributed according to a stable distribution. So intuitively, I think the class of Gaussian scale mixture would offer better fitting flexibility, although the learning/inference may be much harder.
(Aug 20 '11 at 15:20)
Li Tang
