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The horseshoe prior has proven to be a noteworthy alternative for sparseBayesian estimation, but as shown in this paper, the results can be sensitiveto the prior choice for the global shrinkage hyperparameter. We argue that theprevious default choices are dubious due to their tendency to favor solutionswith more unshrunk coefficients than we typically expect a priori. This canlead to bad results if this parameter is not strongly identified by data. Wederive the relationship between the global parameter and the effective numberof nonzeros in the coefficient vector, and show an easy and intuitive way ofsetting up the prior for the global parameter based on our prior beliefs aboutthe number of nonzero coefficients in the model. The results on real world datashow that one can benefit greatly -- in terms of improved parameter estimates,prediction accuracy, and reduced computation time -- from transforming even acrude guess for the number of nonzero coefficients into the prior for theglobal parameter using our framework.

On the Hyperprior Choice for the Global Shrinkage Parameter in the Horseshoe Prior