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

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