Day to day, the biggest problem I encounter in statistical practice is convincing colleagues and customers who do not know the details of methods, that the methods and their inferences are legitimate. Some of the methods are more easily understood than others, and that has become a big part of how I find I need to practice.

]]>You mentioned different kinds of estimation methods for the hyperparameter alpha including Bayesian ones.

I recently saw a paper on genomic selection (Fang et al, 2012, Theoretical & Applied Genetics) where the authors put a prior on alpha and then estimated alpha by the mode of its posterior distribution p(alpha/data) via EM.

In that application, the authors implemented a Bayesian Lasso according to the procedure described by Park and Casella (2008) and the parameter of concern was the penalty parameter lambda. The authors put a gamma distribution G(a,b) on lambda**2 with a=0.5 and b=0. This empirical Bayes procedure worked seemingly as well as the complete one on simulated data. ]]>